Like @vivster said, we need major electoral reform if American democracy can ever hope to support more than two major parties. Our electoral system is based on first-past-the-post, winner-take-all rules. Whoever wins the most votes wins the election, even if they only have, say, 35% of the vote. Because of this in nations with only two viable major parties, third parties serve only as a spoiler. In nations with three or more viable parties, this can result in incredibly unrepresentative outcomes in elections. The formation of a large left-leaning party would only serve to siphon votes away from the Democrats, and would only benefit the Republicans. Of course, conservatives would absolutely love this outcome, as if at least 10% of the Democratic base were to permanently shift their support to a new party separate from the Democrats, it would essentially guarantee Republican hegemony in American politics. Personally, I doubt this new "alternative" will ever amount to anything. Disaffected progressives have had the Green Party for decades as that alternative, and Nader managed to get close to 3 million votes running as a Green in 2000 (more on this in a bit).
Before we even consider forming a major left-wing alternative, we need to change the rules of our electoral system. First and most important of all, FPTP rules need to be eliminated and replaced with ranked-choice voting. That by itself would result in third-party candidates being far, far less likely to serve as spoilers in any election. Additional reforms may be needed as well, including replacing single-member districts for House elections with multi-member districts (which in addition to making the House more representative would make gerrymandering difficult if not nearly impossible) and replacing the Electoral College with a national popular vote for president. But until we get those much-needed reforms, voting third-party does nothing but help the other side. You play the game by the rules as they are, not as you wish they would be. If you don't, the other side wins.
As a progressive, one thing that bugs me most about my side is the willingness of so many of us to vote third-party. While the vast majority of us always vote Democratic, there is a non-trivial minority that has a tendency to vote third-party. Based on exit poll data, for at least the past 20 years, we have done so at an average rate that far exceeds that of conservatives:
The 2000 election saw Ralph Nader siphon votes away from Al Gore. It was sufficient to cost Gore both Florida and New Hampshire. Had only 1% of Nader voters in Florida decided instead to vote for Gore on Election Day, we wouldn't have had Bush as president. After facing the actual reality that was the Bush presidency, progressives became far less likely to vote third-party over the next two presidential election cycles. It didn't help in 2004, as Bush was still sufficiently popular and was successfully able to paint Kerry as a flip-flopper and himself as stronger on the issue of terrorism (plus moral/"culture war" issues helped get out the conservative vote), but the election was still closer than it would have been had Nader done as well among progressives as he did in 2000. By 2008, not just progressives but even most independents and moderates had gotten tired of Bush & the GOP, and Obama won by a considerable margin.
But by 2012, old habits started to re-emerge. The third-party vote expanded somewhat (about 19.8% higher than in 2008), and exit polls showed self-identified liberals voting third-party at a three-to-one rate versus conservatives. It wasn't enough to affect the whole election as Obama was still sufficiently popular with independents, and the progressive third-party vote wasn't distributed evenly, with key swing states showing low rates of voting third-party overall.
And in 2016, we saw a repeat of 2000. If we were to judge electoral performance in terms of improvements from the previous election, third-party candidates were the real winners in 2016, with a 3.5 times increase in their combined vote total from 2012. While there was an across the board increase among all ideological groups and parties in the frequency of third-party voting, the vast majority of that increase was felt among the left and Democratic-leaning moderates. I've said on multiple occasions in various places since the 2016 election that Trump only just barely won that election, with razor-thin victories in Michigan, Wisconsin, and Pennsylvania being the decisive factor. Had Hillary held on to those states, she would have won. Exit poll data suggests that progressive voters voting third-party account for the entire deficit Hillary had against Trump in those states (there was also an increase in self-identified liberals voting Republican, presumably as a protest vote against Hillary). Had more progressives been more willing to vote Democrat, we probably wouldn't be having this discussion right now.
To be fair, disaffected liberals/progressives refusing to vote Democratic are not the only issue at hand. Gore and especially Hillary could have campaigned better than they did. Hillary herself was the target of constant attacks by the right (and even some elements on the left) since the early 90s, which obviously contributed to her relatively poor favorability among the general population. There was the Bush v. Gore case in 2000. And of course there's the distorting effects of the Electoral College, which resulted in both Gore and Hillary losing the election despite winning the national popular vote. But the effects of the voting habits of progressives cannot be denied. They are more likely to refuse to support a Democrat than a conservative is to refuse to support a Republican over a candidate's inability to pass some litmus test for ideological purity. Whether it was Nader voters in 2000 or angry "Bernie or Bust"-ers in 2016, progressives refusing to vote Democratic has been perhaps the deciding factor determining the outcome of several key elections in critical swing states. If progressives consistently voted third-party at a rate of only 1% instead of 3-7% like in three of the past five elections, Democrats likely would have won every election this century.
Now, I fully understand the disappointment many progressives feel with the Democratic Party. I wasn't a huge fan of Hillary even though I voted for her. I'm not even a huge fan of Biden even though I will be voting for him. I voted for Bernie in the primaries both this year and in 2016. But we have to realize that we share the Democratic base with a large portion of non-progressives. Not just the U.S. as a whole, but even the Democratic base in specific is not as left-leaning as a lot of progressives would prefer. According to Gallup, while the Democratic base has been gradually moving leftward since the 90s, moderates were a plurality as recently as the mid 00s, and it wasn't until very recently that self-identified "liberals" accounted for a majority. Meanwhile, the GOP had already been majority conservative for a very long time, and has been moving further to the right over time, with nearly three-quarters of Republicans self-identifying as "conservative." Interestingly, the ideological makeup of independents hasn't budged much, showing that the net decline in Americans identifying as "moderate" has been within people who identify as belonging to one party or the other. Polarization has been asymmetrical in America since at least the 90s, and we've had an obvious right-wing GOP up against a relatively centrist Democratic party. But that is changing, slowly but surely.
If I were to offer advice to progressives who are still thinking of voting third-party (most of them still quite young; the under-30 demo has long been statistically far more likely to vote third-party than older voters), it would be this: Wait. Be patient, young padawan. Work with what you have now. The Democratic Party is moving in an increasingly leftward direction, and eventually that ideal progressive you want will win the nomination (maybe AOC in 2028?). If you didn't get your ideal candidate this time, vote Democratic anyway. Don't even think of it as "voting for the lesser of two evils." Just remove that thought from your mind. Rather, think about what the GOP stands for, and how much you want to see them lose to keep them from getting their way. Anything that could contribute to Republican victories will only hurt what you care about if it does result in a GOP win. And if the GOP continues to win, they will continue to get more nominations to the Supreme Court, they will continue to work to undermine everything you support, and they continue to move themselves and our government in a rightward direction. At worst, a Biden presidency will keep things from getting worse than they already are. At best, we might actually make strides in undoing some of the damage and getting at least some meaningful reforms passed.
Trump and Pence and McConnell are only symptoms of the rightward shift in the GOP, not the cause. The Republican Party has for the past 40 years been defined by a fusion of the social policies of the Christian right with Reaganomics and other quasi-libertarian economic policies. They've been long primed for authoritarian tendencies and conspiratorial beliefs. They long ago convinced themselves that scientists are lying about climate change or evolution. Now we're seeing GOP candidates who believe in QAnon conspiracies get onto the ballot. The John Birch Society types are now the mainstream in the GOP. Do not underestimate the threat the GOP poses to everything you hold dear. They believe you are the enemy. They do not believe you are a "real" American. Their political pundits and more strident politicians make that abundantly clear. When they call the Democrats and everyone else to their left a "communist" or a "Marxist," they aren't just joking or being hyperbolic. They mean it. Or at least their base means it (it's hard to tell if propagandists ever really believe their own propaganda). You're not going up against a party that can be reasoned, bargained, or negotiated with anymore. Compromise is dead, and they killed it. As long as a Repubilcan is in the White House, we will accomplish nothing. As long as the GOP has a majority in the Senate, we will accomplish nothing. It's that asymmetrical polarization in effect. The only way to stop the Republican agenda from making any gains is by winning elections. Progressives really need to fully understand what they are up against with the modern GOP. I had hoped Trump's incompetence, disregard for norms, and authoritarian tendencies would make that abundantly clear, but for some it hasn't. While polls suggest that most progressives that didn't vote Hillary in 2016 will vote Biden this year, there are still plenty of vocal progressives who think it makes perfect sense to not vote Biden because he's not their ideal progressive candidate.
I understand the temptation to cast a protest vote over a moderate candidate winning the Democratic nomination. Perhaps some progressives think it might provide some incentive for the Dems to put forward a more progressive candidate, but it doesn't, because it's not the DNC picking who wins. It's your fellow Democratic primary voters. They chose Hillary. They chose Biden. The party base is still sufficiently centrist to where moderate establishment candidates are favored (and let's not forget that Bernie is not a Democrat). Older voters (especially over-30 African-American voters) in Democratic primaries in particular heavily favor moderate establishment candidates. Their voice matters, too. Potentially costing the Democrats elections by voting third-party to protest how most Democratic primary voters voted will not help you, nor will it compel the party base or leadership to change to better suit your desires. If we want to reform the Democratic Party to become less like the centrist DNC and more like the Congressional Progressive Caucus, the most constructive means of doing so is through the primary process. Also, do more to convince more moderate Democrats you know to vote progressive. It's possible that they may be more progressive-minded than your or they think, and they keep voting for moderate candidates in primaries because they think it makes more sense tactically, or because they think identifying as as a moderate is somehow more "respectable" than identifying as a "liberal," which is seen as a dirty word in American politics by many. Work to transform the party from within, not destroy it by fragmenting it.
Again, the Democratic base keeps moving in a more progressive and less centrist direction. Help keep that momentum going. In the meantime, make sure you do what you can to ensure the Democrats win. Even a moderate Dem will be far better than any Republican. A moderate Democrat is more likely to enact policies that you approve of. If you're a progressive, Biden and the Democrats may give you only 80% of what your want, but the Republicans will give you zero percent of what you want and actively work to undo existing progressive reforms, because the GOP hates everything you support. Our only choices on November 3 are either A) four more years of Trump, or B) a Biden presidency. There will be no other possible outcome. Make the right choice, even if it's not the ideal choice.