Snowe and Murkowski are Republicans In Name Only.
Murkowski briefly came out of the closet when he massively lost a primary and became "independent" then quickly signed on with the Republican caucus so she could do her best to further the Democrat agenda. Nutty, huh? But surely she understood that if she openly admitted her leftish bent she's have to revert to "independent" should she ever want to run for anything again. Dubious whether Alaskan Republicans would have her back but not impossible.
Murkowski is a "she" actually. The name "Lisa" should be a clue. And 51-49 is hardly "massive". And you seem to have left out that she then defeated both parties' candidates in the statewide election. How else would she have reached the Senate?
Nevertheless, Murkowski too, like any other Congresscritter, is elected to represent the people of her state, not the agenda of her party.
If you want we can actually articulate this same rule for all the senators of the other 55 states, but it's not going to change.
Not that there's anything wrong with that, just clearing the record.