It's difficult to answer that, because "socialism" is such a broad term with so many different meanings.
I would say that, at its core, socialism is about state control of the economy and society, and in that case, yes, socialism is un-American, since it is the antithesis of the "life, liberty and the pursuit of happiness" that were the founding ideals of the United States.
Of course, no government of the United States has actually cared about those ideals in the slightest and it's mostly got worse as time has gone on.
The Founding Fathers definitely wanted to keep control away from the government and in the hands of the people because of their negative experience with government across the pond.
Now technically if the people decided to give their power back to the government, it would still be their choice. An idiotic choice in a lot of circumstances, but a choice none the less.
You can't really define the founding fathers in such a simplistic, unified fashion. There was division among their ranks just as their is now between the idea of "big government" and "small government" in the form of the federalists and the anti-federalists. The federalists wanted a strong central government that could tax, raise armies, and possessed an authority that was above that of the states. Anti-federalists were oppose to a strong central government, believing that we should instead be a lose confederation of states. They feared central government because they thought it might give rise to a monarchy.
For a time, the anti-federalists had their way. Through the Articles of Confederation, state power was MUCH stronger, to the point that we had individual currencies and armies. The problem is that it didn't work. We had an opportunity to have a weak central government, but many of the founding fathers disagreed, giving us the constitution and a strong federal government.
Really, what the founding fathers wanted WASN'T a weak central government (though there were certainly many who did), but one ruled by white landowners. The constitution was very carefully crafted to limit the powers of the "unwashed masses" and to protect the country from the tyranny of the majority, which they worried would make the wealthy ruling elite largely irrelevant in government. Hence the electoral college and the original intentions of the Senate (a governing body that was not directly elected, but rather chosen by state goverments, nothing not changed until the early 20th century): they were a means to protect the elite wealthy upper class from the masses.
Of course, this last thing is something that's been slowly chipped away at for two centuries now. But I think it's important that we stop idolizing the Founding Fathers as some uniform body that loved small government (or even a true represenative democracy for that matter). They were just as divided as we are today. They were mostly slaveholders, and even the most progressive among them, if not supporters of slavery, were at least racist by today's standards. They are not neccessarily something to behold as the gold standard these days, something I think they acknowedged given the fact that they created the Constitution to be a living, breathing document that could evolve and change with the days.
For the record, what I've written here is mostly information off the top of my head and I did very minimal research for this. I don't have time to engage in extended debate that will requre such research. I will also acknowledge that I've simplified many things that cannot be properly fleshed out in a forum post.
I'm sure an argument can be made that, despite the differences between federalists and anti-federalists, both would still be considered small government by today's standards. This is something I think I'd agree with. But keep in mind that the world of 1787 was a very different world from today, a world where the government could afford to be less interferring with people's lives. Those were the days before we had steam boats that, if mismanaged, could give thousands of people (which they did, including after the first toothless government regulations were passed regarding them in the 1830s. The following decade saw passage of the first government regulations with TEETH, which played a role in finally bringing dangerous steam boat transportation under control). The days before globalization, before a single person could be capable of waging mass murder with a single weapon, before the existence of mass media, of major multinational corporations and all sorts of other things. Hell, before INDUSTRIALIZATION. But one thing I hope people take away from this, if they even read it, is that you can't define the founding fathers as a singular entity. So please, don't.