“What you want to do is destroy this guy’s life, hold this seat open and hope you win in 2020,” Mr. Graham charged, referring to the next presidential election. “You want this seat? I hope you never get it.”

Though Judge Kavanaugh’s nomination was approved Friday afternoon by the Senate Judiciary Committee on a straight party-line vote, Senator Jeff Flake, Republican of Arizona, provided some drama by announcing that he and a few other senators would withhold their support on confirmation unless a new F.B.I. investigation was ordered to explore the accusations that Mr. Kavanaugh assaulted a woman at a teenage gathering.

Republican leaders had resisted opening such an investigation for days but had no choice but to accede to Mr. Flake’s demand because they lacked the necessary votes without him. Still, the leaders were keeping the machinery of the nomination moving to be ready to force a final vote as soon as the F.B.I. reports back within a week as directed.

The 2016 fight over Mr. Obama’s nominee is unanimously seen as benefiting Republicans in that year’s elections. By holding open the vacancy created by the death of Justice Antonin Scalia, Senator Mitch McConnell, Republican of Kentucky and the majority leader, provided a strong election-year motivation for conservative voters who ended up supporting Mr. Trump so he could fill the seat instead of Hillary Clinton, a Democrat. Mr. Trump won and Republicans held the Senate majority despite their own concerns that they might lose it.

But the political implications of moving ahead on Mr. Kavanaugh with such charged questions swirling around him could play out differently in the midterm elections in November. Republicans are already facing a significant gender gap in public polling, and a decision to confirm Judge Kavanaugh despite the compelling testimony of Christine Blasey Ford that he assaulted her when they were teenagers could exacerbate their struggles with female voters.

Despite a Senate electoral map that works against them, Democrats could capitalize on the court fight to put control of the chamber within reach while also helping the party in its more likely push to gain control of the House.