The path forward remains unclear, but House backers and critics of the $700 billion bailout bill that failed to pass Monday are signaling hope for a new deal by the week’s end.

A Democratic leadership aide said bipartisan talks are ongoing and that phone calls “happened last night and this morning.” Senior GOP aides said they are still trying to figure out when meetings will take place.

“We are all committed to finding a resolution to this issue and finding a resolution to it by week’s end,” Rep. Marsha Blackburn (R-Tenn.) said Tuesday on MSNBC.

Blackburn, a member of the Financial Services Committee and the conservative Republican Study Committee, outlined a list of items that could bring more Republicans on board. These include Federal Deposit Insurance Corp. insurance increases, repatriation of profits from U.S. companies with money earned offshore and 5 percent spending cuts across government agencies, which translates into $103 billion.

“The American people want to make sure they are not the rescuer of first resort,” the Tennessee Republican said. “There are so many free-market-oriented portions of this proposal … that are still there.”

Democratic presidential candidate Sen. Barack Obama (Ill.) said Tuesday that he supports raising the FDIC limit, a proposal backed by some House Republicans. He said he will take up the issue with Congressional leaders; specifically, he called for raising limits from $100,000 to $250,000, which would aid small-business owners.

Rep. Joe Crowley (N.Y.), vice chairman of the New Democrat Coalition, was confident House leaders will be able to get a majority vote “on Thursday or later this week.”

“We will. We will. We will,” Crowley said on MSNBC.

The key is to convince at least 12 more GOP Members to support the bill because “really it was the Republican side that came up short here. What do we have to do to convince the other side that this needs to be done and it needs to be done right away,” Crowley said.