"I have not started counting anything but I feel good," Clyburn said after the meeting with conservative Blue Dog Dems.
Clyburn indicated that he thought a majority of the Democratic Caucus supported the $700 billion package.
"I think it's improved enormously," Rep. Jane Harman (D-Calif.) said of the new bill. Harman, who attended two separate meetings with party leaders, said she was "leaning 'yes'" on the legislation.
Rep. Peter DeFazio (D-Ore.) remains part of a hard-core band of Democrats who oppose the package.
DeFazio criticized Democratic leaders for essentially agreeing to the original proposal offered by Treasury Secretary Henry Paulson more than a week ago.
DeFazio said Paulson, formed head of Goldman Sachs, "created this weapon of mass destruction, and now he's there saying he's the only one who can dismantle it."