A few of them could easily win electoral votes in a Presidential election, thanks to our much-maligned but in my opinion geographically-sound and well thought-out electoral college system.  If a candidate fails to reach the majority # of electoral votes the election returns to Congress, which has decided US Presidential elections in the past.  At that moment your ability to form coalitions with other parties would become very important.

Most important culturally the existing "Democrat" and "Republican" type parties would essentially remain with less conflicted bases and would likely be relatively the two largest parties, preserving a significant amount of the existing political climate.  The key is that the incentive for say left wing Democrats to throw in their hat with them is reduced because the liklihood of a rightwinger getting elected is still about the same as it is today.  The difference is now their values are actually represented, potentially growing and there is an actual platform.

A Progressive/Green coalition party in the US, if able to steal the left wing of the Democratic party, would be very legitimately powerful immediately.  Consider that they would most likely have a couple sitting senators and a number of congressman from day one.