Here we go again. 
Nobody is trying to "restrict" gay marriage. The reality-based among us just don't want ersatz marriage to be recognized by law. The unfounded* assertion that they don't harm society is irrelevant, as "it doesn't harm society" is no reason for government to officially condone private behavior. Such "marriages" have no positive effect, either, so government has no place there.
So long as government hands out special privileges based on marriage status, they have a duty to be non-discriminatory about it, as long both individuals involved are consenting adults. Where is the government's place to deny things like death benefits, survivorship, inheritance, default power of attorney, hospital visitation rights, tax breaks, etc. based on something like the sex of the individuals involved?
The fact of the matter is that the vast majority of the newer generations agree with me, and by ignoring this cultural shift the Republican party is going to find it harder and harder to win elections as they are more and more (and, in this case,
justifiably) painted as the party of bigotry and hate. You can't have the government running around peeking into people's bedrooms to make sure they are inserting the correct part into the correct slot and try and claim you are for freedom and smaller government. People will rightly see that as hypocritical, and you lose votes because of it.
And as Strings said, the abortion debate is another problem; not so much as being against abortion in and of itself (there are still enough people that dislike it that it isn't necessarily losing issue), but the way candidates talk about. Akin and that moron in Indiana were probably one of the single biggest reasons that Romney lost. Instead of keeping their traps shut and giving a boilerplate response, they had to ham-fistedly drag religion into it (and/or confirm the complete and uttler lack of "reality based" scientific knowledge, in Akin's case) in such a way as if to confirm every single bit of the idiotic "war on women" meme that the left successfully spread, especially when Romney failed to distance himself adequately.
Barring a massive unexpected cultural shift, there really isn't going to be any movement on how we deal with abortion. As such, Republicans really ought to put it on the back burner and focus in fiscal issues, instead of getting distracted like a bunch of ADHD squirrels and making themselves look like idiots every time it comes up.
The third big problem is immigration; this issue is probably why Florida went blue. Republicans need to figure out a way to approach it that doesn't make the Democrat's job of painting them as xenophobic racists any easier. Actual, effective immigration reform - making immigration easier while enforcing the law more effectively - would be a good start. Being majority practicing Catholics, Hispanics actually tend to be fairly conservative, so if you can figure out a way not to repulse them they can be lured to the Republican party quite easily.
Fix those three problems, and Republicans would find it much easier to actually win elections. The fiscal end of their platform tends to be a net plus for them, but these three issues - all of them social issues - are absolutely killing them nationally.
