When Senator Mark Pryor, the embattled Democrat from Arkansas, produced an ad last month touting the Affordable Care Act’s health coverage guarantee, a thousand Republican party operatives bombarded his campaign with the word "Obamacare." Pryor didn’t voluntarily pin a scarlet "O" on his campaign, so Republicans did it for him. Fast forward to last week, when Michigan Governor Rick Snyder raised a glass to the “outstanding progress” of his state’s Medicaid expansion, which has already enrolled nearly 400,000 new beneficiaries, and those same GOP operatives sat on their hands.

The upshot is simple. Remove the moniker, and the component benefits of the Affordable Care Act become real political assets. The moniker itself remains unpopular, though. Indeed, what remains of the campaign to repeal the Affordable Care Act is the blind faith that a rose by the name Obamacare will spontaneously putrefy. But though outright repeal has become impossible, Republicans still understand that any catchall for health care reform is a useful way to channel broader unhappiness with the president himself. The enduring unpopularity of reform as a whole is a testament to that fact, and to the likelihood that—absent an Obama favorability surge—these numbers won’t change much for the next couple years. They might never change at all.

The challenge for the next Democratic presidential nominee is thus to break the psychic link—to reshape the way the public thinks about health reform as something more than just a proxy for Obama. And whether she realizes it or not, Hillary Clinton has made a strong case that a female candidate will be better suited to the task than a male candidate.

Last Thursday, Clinton joined a Center for American Progress panel about women’s economic security, focused mainly on gendered issues like equal pay and child care. But Obamacare fits neatly into the same framework. And if a broad category of issues pertaining to gender equity can redound to the Democrats’ political advantage—as Clinton’s appearance at the event suggests—then Obamacare can, too.

As Matt Yglesias observed at Vox last week, in our political discourse, we tend to lump all “women’s issues” together into the same category as culture war flashpoints like abortion. But for public opinion purposes, this is a big mistake. In truth, the politics of things like childcare and wage equality cut very differently than the “social” issues we associate them with, and that's at least in part because they alter the distribution of income. Higher wages, family leave, subsidized childcare—all of these increase women’s income, and, thus, their economic power.