Kavanaugh Could Help G.O.P. in Senate Midterms. But Not in House Races.

And Tom Malinowski, a Democratic challenger in a crucial New Jersey House district, released a digital ad chiding Representative Leonard Lance, the Republican incumbent, for having said days earlier that he was disinclined to believe the allegations against Judge Kavanaugh.

Democratic candidates for governor, including in important battleground states like Florida and Michigan, sided emphatically with Dr. Blasey. Andrew Gillum, the Democratic nominee for governor in Florida, called on Judge Kavanaugh on Thursday to withdraw his nomination.

But Republicans expressed confidence that Judge Kavanaugh’s testimony had rallied voters on the right, shoring up his chances of eventual confirmation and endangering Senate Democrats in red states who vote against him.

In an illustration of how delicate the issue is in important Senate races, Senator Heidi Heitkamp, Democrat of North Dakota, released a campaign ad late in the week rebuking her Republican challenger, Representative Kevin Cramer, for making disrespectful comments about women. Mr. Cramer has repeatedly expressed doubt about Dr. Blasey’s credibility, and about the significance of her story.

But Ms. Heitkamp has also not stated how she will vote on Judge Kavanaugh’s nomination. Neither has Senator Joe Manchin III of West Virginia, where Mr. Trump was scheduled to appear Saturday night at a rally for Mr. Manchin’s Republican rival.

Chris Jankowski — one of the lead strategists advising the Judicial Crisis Network, the main group advocating Judge Kavanaugh’s confirmation — said the judge’s testimony had effectively rallied red-state voters behind him. Lawmakers from those states would suffer for opposing the nominee, Mr. Jankowski said, though he allowed that Republicans could pay a price in congressional and gubernatorial races for his confirmation.

“After yesterday, no Republican senator can expect to run for re-election having not voted for Kavanaugh,” he said. “Senators Manchin and Heitkamp must vote for Kavanaugh to have even a glimmer of hope to win in November. The numbers are just that clear.”

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