Why is there no socialism in the United States? It's a complicated question. You'd probably need something about the length of a book to answer it properly, and you'd have to point out that actually there is some socialism in the United States, just not very much. The little socialist groups never got very far, even during the 1930s when the Great Depression was raging and the country's future was really up for grabs. Then in the 1960s, the counterculture which gripped the nation's youth wasn't at all socialist - it was a very American outburst of individualism and hedonism through which even the children of old leftists defined themselves against their (baffled) parents. Socialism has struggled to even enter the American political stage, whereas in Europe it's never fully left it. So what gives?
The answer, of course, lies in the different historical experiences of America and Europe. Modern political history begins with the Enlightenment and the invention of liberalism, in which people began to question the way society around them was structured and to dream of ways to remake it. This began in feudal Europe as liberal ideas were adopted by the new middle-class in the cities who began to question the rule of aristocrats and monarchs who controlled most of the nation's wealth in the form of massive rural estates and controls on trade. Liberalism - from where we get free-market economics, individual rights, and democracy - gave birth to political movements which wanted to break up the massive estates, put political power in the hands of a much wider group of people, and allow the free market to increase the wealth of all rather than having an economic system that mostly benefitted the already-rich.
This was broadly the idea behind the French Revolution and the American Revolution, yet the former ended in the Terror and Napoleon and the latter ended in the Constitution and Washington. Herein lies the beginning of the answer to our question. Implementing liberal ideas in Europe required a complete remaking of existing society - there were aristocrats whose heads needed chopping off, land which needed to be redistributed, the entrenched power of a conservative church to be taken apart, and angry neighbours in other countries who were worried you might give their own population ideas and so needed fending off. All of this required a powerful state. And so liberals, whose whole agenda was about decentralizing power and vesting it in the people, ended up having to centralize power in the state so that they could make war on the parts of their own society which they disliked.
By comparison, in the United States the whole social structure was already much more liberal. There was a blurring of the line between workers and owners on a scale not seen in Europe, leading to a social consensus which somewhere like France could scarcely imagine. There weren't entrenched aristocrats with private armies, or the same scale of economic monopolies and restrictions designed to keep the rich rich and the poor poor. The society which emerged from the American Revolution had its divisions - many of them regional - but it had a distribution of power and degree of social consensus which made a liberal political system viable from the start without constructing a strong state capable of smashing up the illiberal parts of society (with the exception of the South, which had to be integrated by force later).
It was this sense of unity, consensus and having already achieved a liberal society which proved such an impediment to socialism in America. The long era of social and literal warfare which began in Europe with the French Revolution - the whole modern history of Europe - led to increased spasms of extremism as the counter-revolution and conservatives fought back to defend feudalism against the liberals. When the liberals failed, the socialists appeared claiming that the liberal wasn't radical enough or willing to centralize enough power, or deploy enough violence; what really needed doing was a complete takeover of the economy to not only eject the reactionaries now but to ensure they never came back. In other words, the scale of resistance to the liberal project sparked ever more vicious attacks against those who resisted it, which in turn led to ever more vicious forms of reaction - like fascism, another thing that the U.S. (not coincidently) lacks.
By contrast, in the U.S. there was so little resistance to the liberal project that it never seemed necessary for a more extreme challenger from the left to intervene to ensure the final death of the old society. After all, the old society was already liberal: hence the glorification of America's history and the founding versus the disdain for our pre-liberal history that we usually find in Europe. Europeans view their history as a long process of waking up from a nightmare, whereas Americans view it as a constant struggle to maintain the immaculate Constitution and old values against the corrupting ways of the world. To Europeans, socialism can look like a way of finally putting the old ways down for good; to Americans, it is more likely to look like an alien threat to the City on the Hill. Believing themselves to already have freedom and equality, Americans have been suspicious of socialism as a threat to these things; while believing themselves to have neither, Europeans are more apt to embrace it.
And that is one reason why there is no socialism in the United States.