What would happen if this was the case?
It would probably represent a true refreshing change in politics. Both parties would likely offer this person a committee chairmanship or something to try to sway them over. Basically, it would take a politician who cannot be swayed by perks. Unfortunately, those types of politicians are few and far between.
If they were a top tier candidate, however, in a Senate race, it's likely the party opposite of the opposing candidate would support this person, as it would not allow the other party to expand or maintain its caucus numbers
