Senate Banking, Housing and Urban Affairs Chairman Chris Dodd (D-Conn.) and House Financial Services Chairman Barney Frank (D-Mass.) left a Wednesday meeting with President Barack Obama confident that financial reform will become law by the end of the year, possibly as soon as Memorial Day.

“I’m very hopeful in light of our conversations over the last number of days that we can have a good, strong bill on the floor of the United States Senate within the next month … and have a bill-signing ceremony before this Congress adjourns,” Dodd told reporters after the meeting, which was also attended by Treasury Secretary Timothy Geithner and White House economic adviser Larry Summers..

Asked if he expected to pass the bill by Memorial Day, Dodd said party leaders “said they’d like to do that.” He added that his “hope would be even before then, if possible.”

White House officials are also signaling that they want to wrap up the issue by then.

“The president expects that we will finish financial reform in the next couple of months, certainly by the time we mark the second anniversary of the financial collapse in the early fall,” White House Press Secretary Robert Gibbs said Wednesday.

Gibbs said Obama will likely step up his role in bringing Republicans on board. “The president has been very hands-on regarding financial reform, and I think it is one of the president’s top priorities now,” he said.

Dodd passed his financial reform bill through the Banking Committee on Monday without a single Republican vote. But the Connecticut Democrat signaled that his GOP colleagues may be ready to work together to advance the bill through the full Senate.

“I’ve had some very positive additional conversations” with Banking ranking member Richard Shelby (R-Ala.) “over the last 24 to 48 hours,” Dodd said. Sen. Bob Corker (R-Tenn.) “has been willing to work on these matters and others,” he said.

The House passed Frank’s financial reform proposal in December on a party-line vote. He and Dodd said they will be working together in the coming days to bridge differences between their bills.

There are “a couple of areas of difference, but they are within, I think, reach,” Frank said.

He said he is optimistic about moving forward with their legislation because when lawmakers return after next week’s Congressional recess, “the No. 1 issue before the U.S. Congress will be this bill in the United States Senate.”