There is no guarantee the replacement will fill their predecessor’s committee seats.

“Once there is a new senator sworn into the vacant seat, he or she only gets committee assignments after the Senate adopts a simple resolution,” Reynolds said.

Opponents can in theory hold up that process with a filibuster — continuous, often unnecessary debate on the floor to cause a prolonged delay to a vote. It would take 60 votes to end a filibuster.

For Feinstein, who serves on the Judiciary Committee, that question is particularly important.

Even if she left office, Republicans could prevent her successor — or any Democratic replacement — from filling her seat on the Judiciary Committee, under current Senate rules. That said, taking such a step would be unprecedented and highly provocative.

Democrats could pass a rule change to ensure that Republicans cannot block new senators from committees by requiring a simple majority instead of 60 votes, said Jim Manley, who spent 21 years in the Senate working for Democrats including the late Harry Reid, the former Senate Majority Leader from Nevada.

But Manley noted that Sen. Lindsey Graham (R-S.C.), the leading GOP senator on the Judiciary Committee, said in a recent CNN interview that Republicans would follow precedent if Feinstein resigns.