If they do they will lose. Here's the Gallup people's story on their poll numbers on the topic. Note the story's date is today, howzat for service.
Six in 10 Americans Agree That Gay Sex Should Be Legal
This is an interesting issue because in the last 15 years, it has flipped. In 1987, 35% said "should be legal" and 57% said "should be illegal", and today 62% say "should be legal" and 31% say "should be illegal".
This is the sort of thing I mean when I say things are getting better, things are changing, but we can't see it because we're in it.
The shift from "unacceptable lifestyle" to "acceptable lifestyle" made a similar shift over the last 6 years, from 50-40 to 40-50.
The majority shift from against to in favor of gay marriage or civil unions is happening right now.