Crossing Over of Parties
Political Parties provide various benefits to Members of Congress, including some election support, support in Congress, and positions on various committee. Political parties also serve as ideological homes for Members, and voters are often more attached to a party than to any given candidate. For these reasons, it is fairly uncommon for a Member of Congress to cross over parties, but it is not unheard of.
A member might switch parties, or "cross the floor," for a number of reasons. Some members might switch due to ideological differences with their party. This was the case with Senator Strom Thurmond who, in 1964, switched from the Democratic to Republican party in opposition to the Civil Rights Bills. Others switch for more pragmatic reasons, such as to gain more power in Congress or to gain reelection. Richard Shelby, a relatively conservative Democrat Senator switched to the Republican Party in 1994 after they gained a majority in the Senate, and went on receive high profile committee appointments.
Crossing over can cause difficulties. For example, when Ben Nighthorse Campbell crossed to the Republican party after being elected as a Democratic Senator, much of his Congressional staff quit. Others who have crossed over have found success: Senator Joe Lieberman served as a Democrat and even ran as the Democratic Vice Presidential nominee in 2000, but after losing the Democratic primary in his home state of Connecticut, ran and was elected as an Independent. He eventually supported the 2008 Republican presidential ticket.
Joe Lieberman and John McCain
Senator Lieberman was a Democrat, then crossed over as an Independent, then endorsed a Republican presidential candidate.