(Bloomberg) -- California Governor Gavin Newsom faces a thorny political dilemma over who to chose to replace the late Senator Dianne Feinstein in a heavily Democratic state where a fiercely competitive 2024 Senate primary race is already underway. 

Newsom, a Democrat, has already indicated he’d pick a caretaker to serve out Feinstein’s term to avoid tipping the scales in that primary. He’s also said he would choose a Black woman, a nod to Kamala Harris, who stepped down as California senator in 2021 to be vice president. 

Those two criteria seem to point to California Secretary of State Shirley Weber. She took that office in 201 when Newsom picked her to replace Alex Padilla, whom Newsom had tapped to fill the Senate seat vacated by Harris. 

But Representative Barbara Lee, who is Black and is a candidate in the 2024 Senate race, criticized Newsom’s comments that he would name a Black woman only to serve as a caretaker as “insulting.”

Representatives Adam Schiff and Katie Porter, two of the party’s best fundraisers, are also vying for the seat in what is expected to be one of the most expensive Senate primaries ever.

Newsom’s choice comes as he has been raising his national profile, potentially with eyes on the White House in 2028. He’s scheduled a Fox News debate with Florida Governor Ron DeSantis, who is trailing former President Donald Trump for the 2024 GOP nomination. 

Other picks that fit Newsom’s criteria include Holly J. Mitchell, a Los Angeles County supervisor, and Angela Glover Blackwell, an attorney and civil rights advocate.

Read more: Dianne Feinstein, Longest-Serving Female Senator, Dies at 90 

Newsom hasn’t said when he would appoint Feinstein’s successor, but he’ll be under pressure to move quickly as Democrats now hold just a one-seat majority, and that includes Kyrsten Sinema of Arizona, who left the party to become an independent but still aligns with Democrats for control of the chamber. 

Democrats already are facing turmoil with most Democratic senators having asked New Jersey Senator Robert Menendez to resign after his indictment on federal corruption charges. He told his colleagues at a meeting Thursday he would remain in the Senate, and has denied wrongdoing.

Feinstein’s death could temporarily stall controversial nominations in the Senate, particularly in the Judiciary Committee. It’s not likely to affect the government shutdown fight; Feinstein was one of 76 senators to vote Thursday to advance legislation to keep the government open — her last vote before she died.

Republicans blocked a Democratic plan to temporarily replace Feinstein on the Judiciary Committee this year when she was suffering from shingles, but several Republican senators said Friday they would not try to block her from being replaced by Democrats this time around.

“The problem before was there wasn’t a true vacancy,” said Senator John Cornyn of Texas, a member of the panel.

--With assistance from Erik Wasson.

(Updates with context and details starting in the eighth paragraph.)

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