“It’s a little bit of a tricky balance Democrats are going to have to think through,” said Dan Sena, a Democratic strategist who oversaw the party’s takeover of the House of Representatives in 2018.

“Your base is going to want you to stand up and fight for a seat basically viewed as a Democratic-leaning seat,” Mr. Sena added. But depending on how the battle unfolds, he warned, it may “put people in hyperpartisan corners,” which could endanger Democratic gains with swing voters.

Biden campaign officials are wary of any lines of criticism of Judge Barrett’s deeply conservative background that could be perceived as personal attacks…

“She’s a woman, but the most important fact is that she’s for getting rid of Roe v. Wade and the Affordable Care Act and has positions that will hurt millions of women,” said Josh Schwerin, a spokesman for Priorities USA, a leading pro-Biden super PAC. “If Republicans think that just by putting up a woman they are checking a box that will help them win back suburban women, they’re wrong.”