The political calculus could be simpler for Democrats if Judge Kavanaugh appears almost certain to be confirmed. If the Republican caucus is bound to ultimately fall in line and approve Mr. Trump’s choice on a party-line vote, then some Democrats would prefer not see their most endangered incumbents hectored by liberal donors and activists for what would be only a show of symbolic opposition.

“Our base doesn’t like hearing this, but it comes down to math: You either have the votes or you don’t,” said Jim Manley, a former Senate Democratic aide. “And I’m not so sure the votes are there to beat Brett Kavanaugh.”

Or as Senator Roy Blunt, a Missouri Republican, put it: “It’s easier to be the 53rd vote than the 50th vote.”

But in House campaigns and some state-level races, the nomination is resonating very differently.