Pelosi, who has represented her district since 1987, is vying to become the first woman to make it that high in the House leadership. Her opponent to be the Democrats' whip is Rep. Steny H. Hoyer of Maryland, who has been in Congress for 20 years.
House Democrats will vote Wednesday by secret ballot.
The top Democrat in the House is Minority Leader Richard A. Gephardt of Missouri.
Bonior, 56, will step down as whip Jan. 15 to focus on his campaign to be governor of Michigan. He will remain in the House until his term ends at the end of 2002. He has been Democratic whip since defeating Hoyer in 1991.
In backing Pelosi, Bonior said the whip sometimes has to enforce party discipline and sometimes has to be gently persuasive. "Nancy Pelosi can do both," Bonior said.
Pelosi, 61, claims the support of 120 colleagues. All but one of California's 32 Democrats--the largest delegation in the House--back her. Rep. Ellen O. Tauscher of Alamo is backing Hoyer.
Pelosi raises money for Democratic House candidates and is the ranking Democrat on the House Intelligence Committee.
Hoyer, 62, has said he counts 100 supporters, including the leaders of the black and Hispanic caucuses as well as the more conservative Blue Dogs and New Democrats. Hoyer is the ranking Democrat on the House Administration Committee and has played a key role recruiting Democratic candidates.