By now I think everyone here knows the basics of the ongoing Trump-Musk melodrama, but in order to make more sense of it all and hopefully add some value to the whole discussion surrounding the hilarity, below I will seek to provide a record chronicling the key events in the feud in the order that they happened followed by some commentary on the broader political implications (because no, this is not actually just about two specific men, but a symptom of factional rifts within the Republican Party reopening in a way that has the potential to alter the voter composition of both parties in the future).
The Old and the Restless
{I debated about the title of this chapter. I wanted to capture the soap opera-like feel of the Trump-Musk feud. The second choice I had in mind was "Waste of our Lives", y'know, combining "Days of our Lives" with the DOGE theme of "eradicating waste, fraud, and abuse" like the Department of Education, access to health care and food for the poor, and scientific research.)
Our saga begins with Musk donning that famous "TRUMP WAS RIGHT ABOUT EVERTYHING" t-shirt and ends with him calling for Trump to be impeached and the Republican Party challenged by a new party of perhaps his own creation.
Although the story really begins back in December with the online budget and immigration policy kerfuffle that briefly occurred between the Musk-aligned DOGE wing of the conservative alliance arguing for immediate spending cuts and a soft approach to biotech capitalists importing workers from abroad and the more Trump-aligned MAGA wing under the leadership of Steve Bannon demanding tax hikes for the rich and opposing the importation of workers in general, BUT for practical purposes I'll confine this summary to events beginning with Musk's decision to step back from DOGE:
1) In late April, it was reported that Tesla's profits plunged 71% in the first quarter of this year compared to the same period last year, corresponding to Elon Musk's time in the White House. Immediately after this revelation, Musk in turn announced that he planned to scale back his direct involvement in DOGE to one or two days a week or so starting in May in order to devote more time and focus to his companies. But while he planned to significantly scale back his time in Washington, he also notably stated that he planned to continue running DOGE in some capacity through the end of the Trump presidency.
2) In mid-May, Musk announced he'd be drastically curtailing his campaign spending in the future.
3) Chainsaw man came out against Trump's signature second-term legislation, the Big Beautiful Bill Act (hereafter the BBBA for short), on the grounds that it didn't hurt the working poor enough to fiscally offset the budgetary impact of continuing tax cuts mostly for rich people and called for deeper public welfare cuts, whereupon he was promptly fired from DOGE.
4) Musk escalated his criticisms of the BBBA, calling it a "disgusting abomination".
5) Trump claimed that Musk's real objection to the BBBA is that it ends consumer subsidies for electric vehicles, including Teslas. This contention, incidentally, has some real credibility. After all, in the intervening period, Tesla, which Musk remains the CEO of, came out with an official statement calling on the government to slow down the elimination of those subsidies.
6) Musk claimed Trump would've lost the November election if not for him and that Trump's global trade war will put the U.S. in a recession in the second half of the year.
7) Trump offered the amusing and satisfying observation that "The easiest way to save money in our Budget, Billions and Billions of Dollars, is to terminate Elon’s Governmental Subsidies and Contracts. I was always surprised that Biden didn’t do it." In other words, he threatened to cancel the corporate welfare Musk and his companies benefit from. Tesla's stock then immediately plummeted 14% in value for its single worst day ever on the market. He also angrily threatened to sell that red Tesla he'd bought on the White House lawn. 
8) Musk went fucking ballistic, calling for Trump to be impeached moments after the closing bell, pledging to decommission the Dragon spacecraft, which is the only craft America has that's capable of reaching the International Space Station (just in case you actually believed he was some kind of national hero for returning those two stranded astronauts earlier this year), claimed that Trump was in the Epstein Files and that that's the real reason they haven't been released, and launched a poll on his X platform gauging support for the establishment of a new political party. 
9) After a user expressed disappointment with the feud and suggested a period of calm, Musk backed off his pledge to decommission Dragon capsules.
10) The White House announced a phone call with Musk was now scheduled for the following morning (a couple days ago, Friday June 6th) like Musk was a foreign head of state.
11) The Trump-Musk diplomatic rapprochement apparently failed, as Trump went on to claim that his relationship with Musk was over.
And that's where we are. Think I got all that in the proper chronological order anyway.
The Significance
As I was saying back in April...
"...the Republican Party electoral coalition is at all times composed of two basic factions: the social conservatives and the fiscal conservatives. There are of course innumerable smaller groupings within those two, but that is how they group up together overall. The DOGE-aligned side of that equation -- people who are bigger fans of Elon Musk than of Donald Trump -- are today's fiscal conservatives, or libertarians; the business-aligned section of the coalition. They are essentially the next generation of the old GOP establishment. They've made their peace with MAGA, but hold some distinct views here and there and are different people from the core MAGA crowd at the end of the day. They're younger, richer, and more lopsidedly male. They are the predominant group in the so-called online "manosphere" of male podcast listeners and generally less politically involved or partisan. They care more about balanced budgets and anti-feminism than anything else (well and Covid restrictions back when those were a thing) and are tech futurists. MAGA is, at its core, older, more middle class, and more concerned with globalism than other issues. Core MAGA is more socially conservative overall (the religious right can also be considered part of core MAGA at this point, having completely made its peace with the original movement) and less concerned with taxation rates and balanced budgets and may even support common sense ideas like raising the minimum wage and legislation to make labor organizing easier. They are in fact disproportionately represented in some male-dominated labor unions today. MAGA and DOGE are formally allied in the current administration, but there is at least some natural tension between their goals out in the wilds of the real world beyond the White House."
Musk is trying to really energize the fiscal conservative wing -- the Freedom Caucus people and the corresponding demographics -- with his chainsaw-wielding enthusiasm for butchering the working poor while he takes billions in taxpayer money for himself, and with his demands for free trade and the automation of manufacturing jobs while Trump stands for trade war, sometimes restraining automation for the sake of jobs (e.g. remember his stand with the striking dock workers back at the start of the year over the issue of automation), and has been known to briefly oppose the Medicaid cuts and even call for allowing the top marginal income tax rate he doesn't pay to rise before being promptly corrected by House leadership and moving back to an acceptable Republican position on those matters. In Trump's corner of these debates resides the United Auto Workers, the United Steelworkers, the Longshoremen, the Teamsters, the Screen Actors Guild, and more. In chainsaw man's corner resides the Wall Street Journal, The Economist, and the various business lobbies. You get the picture. That is the sense in which the question of who emerges the social victor in this melodrama matters for the future of our politics in general. According to an early survey on the subject (shared earlier by Ryuu), Trump is winning the spat by a landslide among Republicans, with 71% of them favoring his position compared to just 6% favoring that of Musk. He enjoys an even bigger advantage among the women. Amongst the larger public outside the GOP, ambivalence prevails.
My greatest fear, frankly, is that Elon Musk represents the future...of the Democratic Party. You may not think that's possible, but I do. Looking at the demographic breakdown of the aforementioned survey by party alignment, for example, you will notice that Musk is more popular among Democrats than he is among Republicans at the moment and Trump seems to think it important to warn Musk against funding Democrats in next year's midterm elections. Musk seems to have pretty well torched any future he might've had in Republican Party politics by picking such a brutal fight with a president they dearly love and Democrats are inclined toward a high level of skepticism, but nonetheless...nonetheless the margins matter here, IMO. The slice of "moderate" voters who like Musk better than Trump is the one the "moderate" Democrats feel the party should be focused on reaching out to and it would be but a continuation of their efforts over the last decade or so to consolidate the support of suburban professionals and business owners while the Republicans focus more on winning over blue collar punch clock workers. I wonder if in another decade or two the Democratic Party's politics might be more fully bourgeoisified and consequently look somewhat similar to the way Musk's do right now. And conversely, perhaps Republican Party politics will be somewhat more fully proletarianized and popular with the labor movement broadly, embracing the corresponding economic ideas more completely under future, post-Trump leadership. That is what makes this cultural battle between the tribal populists and the technocratic futurists of the GOP, of which the Trump-Musk feud is a microcosm and manifestation of, interesting to me.