New polling out of California suggests that a majority of voters — including self-described Democrats — think the state’s senior senator, Dianne Feinstein, who recently returned to Washington after an absence of several months for health reasons, is no longer fit to serve.

Commissioned by Los Angeles Times and conducted by the UC Berkeley Center of Governmental Studies, the poll found that nearly two-thirds of the state’s voters, and 52 percent of Democrats, agreed with the statement that the 89-year-old senator’s “latest illness underlines the fact that she is no longer fit to continue serving in the U.S. Senate.” 

Respondents were in less agreement about what Ms. Feinstein should do. Some 42 percent said she should resign immediately and let Governor Newsom appoint a replacement, while 27 percent said she should serve out the remainder of her term and retire following the 2024 election. About 31 percent described themselves as undecided.

“The poll clearly shows that while support for Senator Feinstein has waned considerably since 2018, there is no clear consensus about how the process should play  out,  and  this  will  impact  her  ability  to  connect  with  voters  and  serve  her  constituents over the remainder of her term,” the Berkeley center’s co-director, G. Christina Mora, said. 

The poll comes amid reports that the senator’s staffers have gone to great lengths to keep Ms. Feinstein away from the prying eyes and ears of reporters and photographers on Capitol Hill, and even asked the Capitol Police to keep members of the press as far away from her as possible. One staffer reportedly even hid her wheelchair behind a pillar last week to keep it from appearing in photos of the senator as she left the building.

A Los Angeles Times staff photographer who covers Congress, Kent Nishimura, said members of Ms. Feinstein’s staff — especially Speaker Pelosi’s daughter, Nancy Corinne Prowda — use every trick in the book to stay out of sight and at a distance from members of the press.

“Her staff’s efforts to protect the former San Francisco mayor from scrutiny have intensified since her return,” Mr. Nishimura wrote in a column for the paper on Wednesday. “In committee meetings, her public remarks have been limited and she is always surrounded by staff. They also often form a human barrier between her and the press corps, with one staffer pushing her wheelchair while others shout at photographers to move out of the way.”

Mr. Nishimura singled out Ms. Prowda, Ms. Pelosi’s eldest daughter, as being particularly aggressive in her interference. While Ms. Pelosi has been friends with Ms. Feinstein for decades, the speculation on Capitol Hill is that the former wants the latter to finish our her term in order to avoid allowing Mr. Newsom to select her successor.

Given the chance, Mr. Newsom has pledged to appoint a Black woman to the seat, and the only Black woman currently in the hotly contested race to succeed Ms. Feinstein is Barbara Lee, a congresswoman of Oakland. Ms. Pelosi has endorsed Representative Adam Schiff, a longtime protégé, in the race. Were Mr. Newsom to name Ms. Lee before the 2024 election, she would enjoy a considerable advantage over Mr. Schiff in the race.

According to a report from the Associated Press, Mr. Newsom is said to be toying with the idea of appointing a television star, Oprah Winfrey, to the seat if Ms. Feinstein is unable to finish out her term. Such an appointment would be as a caretaker of sorts, with Ms. Winfrey not running for re-election but merely holding the seat long enough for a replacement to be selected by the electorate in 2024.

The Berkeley poll suggests that the race to replace Ms. Feinstein is wide open. The only serious Republican in the contest, attorney Eric Early, is polling at about 18 percent, and Congresswoman Katie Porter, a Democrat, is at about 17 percent. Mr. Schiff enjoyed the support of 14 percent of respondents to the poll, and Ms. Lee trails at 9 percent. Some 32 percent said they were undecided and 10 percent said they wanted “someone else.”