With the economy showing fresh signs of weakness, the measure advanced past a key hurdle on a 223-205 vote.
An Associated Press tally showed 16 lawmakers who sent an earlier bailout bill to unexpected defeat on Monday had changed their minds and would vote in favor of the revised legislation, more than the dozen needed. Officials said changes made to the measure had sparked a far smaller number of defections among previous supporters.
"I'm optimistic about today. We're not going to take anything for granted but it's time to act," said House Republican Leader John Boehner of Ohio.
"I think it will pass," agreed Rep. Jim Clyburn, the chief Democratic vote-counter, as debate unfolded in the House chamber.
The Senate passed the measure earlier in the week on a bipartisan vote of 74-25.
"No matter what we do or what we pass, there are still tough times out there. People are mad -- I'm mad," said Republican Rep. J. Gresham Barrett of South Carolina, who opposed the measure the first time it came to a vote. Now, he said, "We have to act. We have to act now."
Rep. John Lewis, D-Ga., another convert, said, "I have decided that the cost of doing nothing is greater than the cost of doing something."