On a conference call with reporters just now, DNC chairwoman Debbie Wasserman Schultz called on Mitt Romney to state whether he supports the Paycheck Fairness Act — which the Senate is set to vote on soon, making it the new front in the raging political war over women.

Wasserman Schultz pointed out that Romney has not said whether he would have signed the 2009 Lily Ledbetter Act, which made it easier for people to challenge pay discrimination. (Romney has said he has no intention to overturn it, and his campaign has said he suppports “pay equity” in principle.)

The Paycheck Fairness Act — which would update and strengthen the Equal Pay Act of 1963 — was defeated by solid Republican opposition in the Senate two years ago, meaning it is not law, but it could become law when it is voted on in coming weeks.

So Romney’s stance could actually matter to the vote’s outcome — and this creates a test for him. Does he break with Republican Senators and the U.S. Chamber of Commerce to support the measure? Or does he break with his own rhetorical support for “pay equity” and oppose it, perhaps damaging him further among female swing voters?

“It speaks volumes that Romney can’t say whether or not he would have signed [Lily Ledbetter] into law,” Wasserman Schultz said on the call. “And so I feel quite certain that he also opposes the Paycheck Fairness Act.”

“That bill is not law, because Republicans blocked it,” she continued. “Republicans have absolutely no interest in ensuring pay equity in this country ... Romney would turn back the clock and leave us stagnant and stifled.”

The other important dimension to this: The Romney campaign has repeatedly argued that the dust-ups over cultural issues that dominated the GOP primary won’t harm him among women in the general election, because they are primarily interested in jobs and the economy, where Obama has let them down. In response, Dems have shifted from their focus on cultural issues to highlight areas where Romney is not on the side of women on economic issues — such as pay equity.

If Dems continue to pressure Romney on the Paycheck Fairness Act, it could elevate the issue’s profile and lead Senate Dems to prioritize the coming vote on it. At the same time, if Romney does support the proposal, it makes it more likely that a few Senate Republicans could come out in support of it and possibly help pass it into law. So this is definitely something to watch.