At his press conference this morning announcing the new shift in contraception policy, Obama said: “I understand that some folks in Washington may want to treat this as another political wedge issue. But it shouldn’t be.”

The irony is that after this announcement, this very well may become a wedge issue — against Republicans.

That’s because anyone who comes out against the proposal Obama outlined today will be asked a simple question: Are you saying that employers should dictate to female employees whether they should or shouldn’t have access to birth control coverage?

The policy announced today would remove religious institutions from any role in providing coverage for birth control for female employees. The transaction would occur directly between women and insurers. Yet here’s how Senator Orrin Hatch, one of the first to oppose today’s announcement, explains his opposition:

“This is about religious freedom, and anything short of a full exemption is no compromise. ...The backlash surrounding the White House’s decision to force religious institutions to act against their beliefs lays that fundamental fact that the President’s health law is unconstitutional to its very core.”

By “full exemption,” is Hatch saying that employers at Catholic hospitals and universities should have the power to dictate to employees that they cannot have any access to contraception coverage? He doesn’t quite say it that way, but it’s unclear how else you would read his statement. And if Dems have their way, officials like Hatch will be pressed to clarify whether this is their position.

Separately, GOP Rep. Roy Blunt recently introduced a measure that would give insurers the right to deny women contraceptive coverage.

These are not stances that will be easy for Republicans like, say, Scott Brown to take. The GOP could very well end up divided on these core issues.

There’s been a ton of commentary to the effect that Obama’s stance on contaception could damage him among Catholic swing voters. For all I know, it’s possible, particularly among church-going, as opposed to secular, catholics. But this is clearly bad politics for Republicans, too.

All the GOP presidential candidates will be expected to double down in opposition to Obama’s new policy. Yet multiple recent polls have shown Obama opening up a sizable lead against Romney among women. What kind of impact do you think GOP opposition to free contraception for female employees of these institutions will have on that gender gap?

By the way, a new poll came out just today illustrating how perilous this position may be among Americans overall. It found that a big majority, 61 percent, approve of “requiring employer health plans to cover birth control for women.” Only 34 percent disapproved. Independents approve 58-34; women, 67-29. Republicans, conservatives, and Tea Partyers all oppose it.

The polling organization that published these findings? Fox News.