Bill Clinton was a common person. While he didn't start his own political party, he radically changed the Democratic party into a more conservative form, and got himself elected President.
Was Bill Clinton appreciably more conservative than Jimmy Carter, the last Dem President before Clinton?
Very much so. Clinton trimmed the welfare rolls, cut the number of federal employees, deregulated finance, deregulated telecom (though Carter was also a major deregulator, having deregulated airlines, trucking, and beer), signed NAFTA, signed DADT, signed DOMA, signed RFRA, passed aggressive violent crime legislation, etc.