"The president says that the jury's out on evolution. Here in New Jersey, we're counting on it."
–Bruce Springsteen, May 21, 2005
"Folks in Dover [PA] aren't sure about evolution. Here in New Jersey, we're counting on it."
–Bruce Springsteen, August, 2005
"This issue [marriage equality] is in a state of evolution."
–Hillary Clinton for Senate spokesperson Karen Dunn, July 3, 2003
"I have been to this point unwilling to sign on to same-sex marriage primarily because of my understandings of the traditional definitions of marriage. But I also think you’re right that attitudes evolve, including mine."
–President Barack Obama, October 27, 2010
"We cannot afford to be imprisoned by politics that say your views are not allowed to grow as you gain knowledge and experience. There’s nothing wrong with acknowledging you’ve changed your mind when your views have evolved. Don’t we pride ourselves on learning by living?"
–Sen. John Kerry, July 10, 2011 op-ed titled, "Politicians have the right to evolve on gay marriage"
“That was my timetable, that was my home state,” Boxer said. “That’s how I evolved. Vice President Biden evolved on his timetable, and President Obama evolved on his timetable.”
–Sen. Barbara Boxer, May 9, 2012
"I support marriage equality because it is the fair and right thing to do. Like many Virginians and Americans, my views on gay marriage have evolved, and this is the inevitable extension of my efforts to promote equality and opportunity for everyone."
–Sen. Mark Warner, March 25, 2013
“I’ve got two young sons who, when I ask them and their friends how they feel about gay marriage, kinda give me one of those looks like, ‘Gosh mom, why are you even asking that question?’ The term ‘evolving view’ has been perhaps overused, but I think it is an appropriate term for me to use.”
–Senator Lisa Murkowski (R-Alaska), March 28, 2013
“I don’t support the gay marriage. My [gay] son is by far one of the most important people in my life. I love him more than I can say. It doesn’t mean that I don’t have respect, it doesn’t mean that I don’t sympathize with some of the issues. It just means I haven’t evolved to that stage.”
–Rep. Matt Salmon (R-Ariz) to KTVK, March 29, 2012
The Washington Post's Rachel Weiner assembled those quotes on "evolving" views on gay marriage, and discusses why the term works so well there:
Evolution implies forward movement and change; once a politician starts to evolve, the implication is that he or she won’t stop. So for Sen. Lisa Murkowski (R-Alaska) to describe herself as “evolving” implies that she will come to one day support gay marriage. Likewise, for Salmon to say he hasn’t evolved implies some failing on his part. …
When politicians say they’ve evolved, it not only gives them political cover; it flatters voters who have changed their views but don’t want to be told that they were ever wrong. …
More proof: Sen. Rand Paul (R-Ky.), trying to push his party on immigration, suggested they “evolve.”
Rand Paul, of course, is has been squirrelly about his views on evolution itself, refusing to even tell a group of home schoolers how old he thinks the earth might be. I doubt you'd get any more of an endorsement of evolution from Sen. Murkowski or Rep. Salmon. It's still nice to know that, however much they may be unsure about evolution, the GOP is counting on it.
When a politician says s/he has evolved on an issue, what s/he means is that the relevant electorate has evolved and now s/he can either openly express or openly deny his/her actual moral beliefs.