The two sides met Monday to craft amendments that will appeal to Republicans by cutting out billions of spending provisions, but add tens of billions of dollars to what is already in the bill for the country's infrastructure, do more for housing and possibly reduce the overall cost of the bill.
The House version totaled $819 billion, while initial drafts of the Senate bill neared $900 billion.
Republicans are also considering an alternative bill that would put more emphasis on tax breaks and would allow qualified borrowers who have not fallen behind on their mortgage payments to refinance into new mortgages with interest rates as low as 4 percent.
If the first vote on an amendment today is an indication, it will require some hard negotating to hammer out a package both sides are willing to live with.
Republicans killed a Democratic effort on a procedural vote add $25 billion to infrastructure repair, which would have brought the total infrastructure spending in the bill to $167 billion. The Democrats needed 60 votes, but fell two votes shorts. Only two Republicans, Sens. Arlen Spector of Pennsylvania and Kit Bond of Missouri, voted with the Democrats. One Democrat, however, Sen. Mary Landrieu of Louisiana, voted with the Republicans.
Senate Minority Leader Mitch McConnell said Republicans blocked the increase for infrastructure spending because "it just expanded the size of the bill."
"We need to pare it down ... rather than have it ballooning upwards," McConnell said.
Referring to size of the proposed bailout, McConnell added, "We need to sober up here and take a look at what we're doing."
Obama had originally hoped to win 80 votes in the Senate but is now hoping to pick up enough Republican votes to claim it has bipartisan support. He has also set a deadline of mid-February for the House and Senate to pass their bills and iron out the differences between the two measures.
He hopes to sign it into law around President's Day, in mid-February.
ABC News' Rick Klein contributed to this report.