Public polls seem to suggest that the birth control fight has the potential to be terrible politics for Republicans — it could be used as wedge issue against the GOP and could help Obama and Dems win women in the numbers they need this fall.

So are Republican strategists who are in the business of winning elections — as opposed to conservative and evangelical groups who see this as a way to prime their support base — worried about this?

I just got off the phone with Whit Ayres, the well-known GOP strategist, and he laid out the counterargument.

He conceded the battle could go either way, but argued Republicans can win if they frame it “in the context of an overweening government mandate that is part of Obamacare and forces religious institutions to do things they fundamentally disagree with.” He argued Republicans must not allow the argument to “devolve into, `are you for or against contraception.’”

Republicans don’t believe the public polling tests the crux of the issue as they hope to define it in the public mind. This week’s Times/CBS poll asks two questions — whether respondents favor a federal requirement that “health insurance plans” cover contraception, and whether they favor requiring “religiously affiliated employers” to cover it. In both cases, large majorities say Yes.

But Ayres — and other GOPers — say this line of questioning misses a key component: Whether they should be required to cover it if so doing violates their moral or religious convictions. He said the response would be very different if pollsters asked whether people “support or oppose the federal government requirement” that institutions or employers “offer health care that violates their fundamental beliefs.”

The Obama accommodation exempts religious institutions from covering contraception. But Republicans insist this is no compromies, because these instiutions are still funding health plans that covers it.

Republicans hope this fight will allow them to advance a key subtext: Obama wants to expand the reach of government into matters of faith and is hostile to religious values. Ayres said the GOP message “plays into the fundamental suspicions that Americans have about Obamacare in the first place,” that this is about “overweening Obamacare sticking its nose where it doesn’t belong.”

It’s my view that this line ultimately won’t square with voter perceptions of Obama’s attitudes towards faith and values, and that the public will prove more sympathetic to the Dem framing of the issue. But this is the message Dems are up against.