Citing a harsh report on missteps at the Smithsonian Institution, Senator Dianne Feinstein declared at a hearing on Tuesday that the museum complex should move quickly to replace its ousted top executive rather than take an estimated six months to a year.

“This represents significant jeopardy to the institution,” said Ms. Feinstein, Democrat of California and chairwoman of the Senate Rules and Administration Committee. “I have a hard time understanding why we need this huge search period. When the cat’s away, the mice play.”