The National Women’s Law Center released a new state-by-state study today on women and the minimum wage, and it calculates that over 250,000 women would get a raise in Kentucky if the minimum wage is raised.

Mitch McConnell opposes raising the minimum wage. His Dem opponent, Alison Lundergan Grimes, supports raising it. And the Grimes campaign is seizing on the data in hopes of steering the campaign towards a discussion of wages and pay equity — turf Dems hope will favor them in an otherwise hostile political climate, particularly in red states.

In an interview, Grimes pollster Mark Mellman noted that the minimum wage would be key to appealing to a crucial demographic — downscale women.

“The minimum wage affects a lot of people — particularly a lot of women — in Kentucky,” Mellman said. “Women are the majority of the vote in Kentucky. As a group, they are more hostile to Mitch McConnell than men are. They are a critically important base for any Democrat, particularly a female Democrat. Downscale voters in these states tend to be very important swing voters — particularly downscale women.”

McConnell’s opposition to a minimum wage hike, Mellman said, “communicates something larger — that he’s not interested in economic opportunity for the middle class or those struggling to join it.”

Of course, if the economy continues to sputter, it could work against Dems. Republicans are seizing on bad jobs numbers to intensify attacks on the Affordable Care Act, which is becoming a kind of stand-in for Big Bad Job-Killing Government under Obama.

Obamacare remains deeply unpopular in Kentucky, even though its exchange has successfully expanded coverage to poor, rural people who desperately need it. Pushed on whether this would be a liability, Mellman said: “Most people in the country don’t want to repeal Obamacare. They want to fix it. That’s where she is.”

Mellman acknowledged Dems expect a fierce attack on Grimes that echos familiar GOP arguments against Dems as job killers, but argued she’ll withstand it, as someone who have never been in Congress and didn’t vote for the health law. “McConnell will talk about taxes and spending,” Mellman said. “But Alison hasn’t voted for taxes. It’s going to be particularly difficult to make the usual Republican case against her.”

By contrast, “McConnell is the symbol of everything that’s wrong with Washington.”

The bigger story here — one we’ll see in other red states — is that Dems hope to win despite Obamacare’s travails by broadening the conversation. The minimum wage, unemployment insurance, and even certain aspects of Obamacare — its expansion of health care to people who lack it — are all part of a storyline that helps Dems, if it can supplant the preferred GOP storyline. As Brian Beutler puts it:

The two most dominant political narratives in the country intersect right here. One is that Obamacare’s a big mess and a political liability for Democrats. The other is that inequality is a huge national challenge, and Republicans’ existing ideological commitments prevent them from addressing it in any concrete way.

Republicans oppose extending UI and the Medicaid expansion, and are attacking the CBO report as proof that expanding health care to people who lack it saps the will to work — all of which risks dragging the conversation on to perilous “free stuff” and “47 percent” turf. Indeed, Mitch McConnell has already dismissed Obamacare’s success in Kentucky by deriding “free health care.” Grimes will avoid picking direct fights over the health law, but she stands up for its expansion of coverage and hits repeal as a threat to take that away from people. Meanwhile, the focus on two fused issues — the minimum wage, and pay equity — will be pressed into service to further emphasize the Dems’ preferred pocketbook narrative.