As has been noted many times in the past, several of the founding fathers didn't have too many good words to say about political parties, the chief among these being George Washington himself who said that they "must be restrained in a popularly elected government because of their tendency to distract the government from their duties, create unfounded jealousies among groups and regions, raise false alarms amongst the people, promote riots and insurrection, and provide foreign nations and interests access to the government where they can impose their will upon the country". Of course, nothing ever came of these criticisms against parties over the ensuing governments, even during the presidency of the openly anti-party (or more correctly, anti-partisan) James Monroe.
However, what would happen if Washington attempted to (and if it's possible, succeeded) in prohibiting the formation of political parties on the national level, especially if it came in the form of an amendment. Of course, there's several boundaries that have to be crossed before such an amendment could come into affect (particularly if it's seen as restricting the freedoms of assembly and the unenumerated right that would become freedom of association), as well as the fact that in the US style of democracy, political 'associations' are almost guaranteed to rise eventually, but what if he managed to get it passed? How would it affect the evolution early American politics (particularly the Second-Party System and Jacksonian Democracy), and more importantly, would it be likely to see such an amendment overruled later down the track (if it even gets passed in the first place)?