Honestly, I don't think many Americans actually understand what Socialism is.
Socialism is the state-ownership of economic machinery; not a redistributive tax system or the presence of a welfare state. To be fair, redistributive tax systems and welfare states can be part of Socialist systems, but they are not its defining feature.
To call Europe a 'Socialist Continent', like many Americans often do, is to severely miss the point.
Since the 1980s and Old Devil C**t Maggie (at least in the UK), the state has been systematically selling off state owned properties (usually to friends and former classmates of the governing party) for cheap. The 'Socialist' Labour party repealed Clause 4 in their charter in 1994 which was their commitment to nationalisation of key industries.
The Tories have just sold off the Royal Mail, effectively at a loss, and are currently working to undermine the NHS so that it can later be sold off in the name of efficiency.
To answer the OP though; No, I don't think the USA will ever have an honest Socialist party, or even the weak, centre-right parties that we have here. Because culturally, the idea of society having a responsibility to care for those who struggle to care for themselves is not part of the American psyche.
The way 'Obamacare', 'Workfare', taxation etc. are treated in the US demonstrates that. In the UK, the Welfare State grew out of the ravages of the 2nd World War and the ruling classes seeing for themselves the appalling conditions the working classes had to face. America never had that meeting of the classes.
And to clarify; when I use the term 'Americans', I am referring to the average person. I am not casting aspersions on any individuals here, nor am I making any assumptions as to what any individual may believe politically as a result of their nationality.