Aside healthcare, there are insignificant ideological differences between this president and the last. Obama even extended the tax cuts for the wealthiest Americans. I'm not sure what you mean by European style mixed economy and whether voters choose that when they elected Obama.
But yea, it's political suicide to appear "socialist", even on many social issues. I honestly even sympathize with the Tea Party on financial matters. Aside Ron Paul the other candidates (Bachman, Palin and related.) are buffoons. I'm just very libertarian. Wall Street is really in the pockets of the Democrats and Republicans don't even believe in free market capitalism anymore. Shame...