Close, but not quite right. Socialism, while having some Athenian roots, really didn’t take hold in any sense until the 1850’s. The Founding Fathers were more worried about a direct democracy allowing a simple majority of voters to make swift changes that trampled rights and liberties (this could go either way on the political spectrum, mind you).
Their intent was for changes to occur slowly and to require a much larger consensus. This, obviously, has had its pros and cons, and shouldn’t necessarily be seen as the end all, be all.