When moderate-to-liberal Republicans have gotten into trouble with their liberal constituents, it has generally been because of their support for more-conservative Republican presidents and other national GOP leaders than because of their opposition to Democratic presidents. When such Republicans alternate between voting with a Democratic president and voting against him, it actually bolsters their reputation for independence. Some of the worst years for liberal Republicans have been 1974, 1982, and 2006 — all years when Republican presidents were unpopular. The moderate Republicans who went down in 1996 were attacked more for their support of Newt Gingrich than their opposition to Bill Clinton.
The only major exception to this trend has been the ladies from Maine, Olympia Snowe and Susan Collins. They managed to prosper in the 1990s despite Gingrich and they were reelected in 2006 and 2008, respectively, despite Bush. Maine still seems to be a place where Rockefeller Republicanism is generally popular, as evidenced by Snowe, Collins, William Cohen, and John McKernan.