At 87, Ms. Feinstein, the oldest member of the Senate, no longer walks through the Capitol without an aide at hand and rarely speaks off the cuff, eschewing national television interviews. Her statements to reporters can require after-the-fact corrections from staff members. Colleagues and Senate aides privately worry that she sometimes appears bewildered or disengaged…

Progressive activists, many of whom argued that Ms. Feinstein badly botched the brutal 2018 confirmation process for Justice Brett M. Kavanaugh and the 2017 hearing on Judge Barrett’s confirmation to an appeals court, have warned that if she stumbles again, they are ready to outright push for her removal.

“This whole process has the potential to provide even further evidence of how Democrats ought to think about making a change in terms of who is running the committee,” said Brian Fallon, a founder of Demand Justice, a liberal advocacy group that lobbies Democrats to prioritize the federal courts.

Republicans, who believe Ms. Feinstein’s handling of the Kavanaugh hearings two years ago helped fire up their base and win them key Senate races, are eager to exploit any of her perceived missteps.