Senate moderates from both parties are trying to cut as much as $100 billion from the economic stimulus package.
Senate Democratic leaders say they hope it can be passed by tomorrow.
Chances of passage appear to hinge on agreement to a series of changes that would trim the size of the bill, which now would cost well over $920 billion.
Senate centrists who met privately say they've made progress.
Republican Susan Collins of Maine, who met with Barack Obama at the White House yesterday, says the president made a "strong case" for a proposal that would cost about $800 billion.
The president has been issuing a series of increasingly dire warnings in recent days. With new jobless claims registering a bigger gain than expected today, Obama said, "The time for action is now."