Republicans thought they could count on an election that would be all about the economy and nothing else, allowing their positions — and divisions — on social issues to recede into the background. But Obama has emerged as the election’s number one culture warrior, endorsing gay marriage, vowing to protect Planned Parenthood, and running ads hammering Republicans over abortion and women’s health.

Democrats obviously got a big assist from Todd Akin’s remarks about “legitimate rape.” Now, with Akin remaining in the Missouri Senate race, Dems are moving to tie Akin to the GOP convention by arguing, in effect, that this is Akin’s party now.

The Obama-allied group American Bridge will unveil a new Web site today called “,” which is designed to demonstrate that many of the speakers at the GOP convention share views on abortion that are quite similar to Akin’s. You can click on the face of any Republican — Paul Ryan, Mike Huckabee, Scott Walker, Jed Bush, Nikki Haley — and scroll through their record of relevant votes or public statements on abortion.

“Todd Akin may be unwelcome in Tampa this week but the policy conclusions he reached will still be well-represented,” emails Rodell Mollineau, the president of American Bridge. “With so many influential members of his Party holding a position in contrast to his own, thank goodness Romney is known for a steadfast adherence to his beliefs.”

The push from the group dovetails with “Romney-Ryan-Akin” messaging from the DNC, which is running full page ads in today’s Tampa Tribune that tie Romney to the abortion views of both Ryan and Akin, who so-sponsored a personhood bill and oppose abortion even in cases of rape and incest. The Ryan/Akin stance is deeply unpopular. A recent CNN poll found that 83 percent of Americans think abortion should be legal in cases of rape or incest.

Skeptics will rightly note that the economy is a far more dominant public concern than abortion in this election. But the election of a Republican president would, in fact, have policy consequences on women’s issues, starting with the small matter of Supreme Court justices. As David Dayen notes today, abortion, women’s rights, and women’s health are on the ballot this fall, whether Republicans like it or not — and the gender gap could loom large in this election.

What’s more, the Dem strategy is about something broader: tarnishing the Republican brand by painting the party as hidebound and backward-looking. That could weigh down the GOP ticket, particularly if Obama can neutralize Romney’s expected advantage on the economy. Romney has said his administration won’t oppose abortion in cases of rape — departing from the Ryan-Akin position — but Dem strategists view the issue as a good way to raise doubts about his commitment to his own stated convictions and his unwillingness to stand up to extreme voices in his party.