Early public-opinion polling shows little evidence of a massive swing against Republicans based on the impending threat to Roe. A CNN survey taken in the immediate aftermath of the leak showed that Americans favored keeping Roe intact by roughly 2 to 1, yet Republicans still enjoyed a seven-point advantage over Democrats when voters were asked about their midterm preferences — a margin that would easily swing both chambers to the GOP.

Democrats insist that will change if the draft ruling becomes official and once candidates and groups start spending their massive campaign war chests on advertising that highlights the threat to reproductive rights. And top party leaders believe that the issue will have special resonance in some of the midterm elections’ top battlegrounds.

“There’s certain states that have even stronger support for Roe v. Wade,” said Sen. Gary Peters (D-Mich.), citing New Hampshire, Nevada and Arizona as places where party research has showed particular salience for abortion rights. “And there’s a very clear contrast between where our candidates are … in those states and the Republican candidates, [who] have taken, for the most part, very extreme views.”