House and Senate Democrats raced Tuesday to salvage a hard-fought deal on financial regulatory reform, but Senate leaders appeared stuck at least one vote shy of the number needed to beat back a near-certain GOP-led filibuster.

Still, House leaders were pushing forward with plans to pass the bill this week and were operating with the understanding that Senate leaders could clear the legislation for President Barack Obama’s signature once the Democratic replacement for the late Sen. Robert Byrd (D-W.Va.) arrives sometime after the July Fourth recess, if not before.

Though House and Senate conferees announced a deal on the legislation last week, they were forced to return to the negotiating table Tuesday when three Senate Republicans — Olympia Snowe and Susan Collins of Maine and Scott Brown of Massachusetts — who supported the Senate version of the bill balked at the conference report’s $19 billion bank and hedge fund tax.

Within hours of Brown announcing his opposition to the language, Senate Banking Chairman Chris Dodd (D-Conn.) told reporters they would likely eliminate the tax and make up the shortfall by putting an end to any further withdrawals of the $700 billion financial industry bailout fund created in 2008. The plan also calls for raising fees on large banks that pay into the Federal Deposit Insurance Corp.

By early evening, the conference committee had reconvened and done just that.

Snowe, Collins and Brown were still publicly noncommittal, but it appeared the deal was likely to secure their votes for the conference report.

However, Dodd still must persuade one Democrat or Republican who opposed the bill last month to switch positions. Even if Dodd shores up the votes of the three Republicans, Byrd’s death early Monday morning leaves Dodd one vote short of the 60 needed to kill another attempted filibuster.

“Obviously I’m talking to a lot of offices and a lot of people to find out where that spot is that will get us to where we need to be going,” Dodd told reporters Tuesday. “We’re very, very close and my hope is we can do it.”

Two Senate Democrats, Maria Cantwell (Wash.) and Russ Feingold (Wis.), voted against the Senate version of the bill.

House Financial Services Chairman Barney Frank (D-Mass.) said Tuesday that Dodd has told him Cantwell may switch her vote to “yes,” and Senate Democratic aides said Cantwell was sending signals that she might flip. However, a Cantwell spokesman would say only that she is reviewing the conference report.

Though a Senate vote this week appeared remote, a vote switch by Cantwell or anyone else who opposed the original bill would obviate the need to wait until Democratic West Virginia Gov. Joe Manchin names Byrd’s replacement. It is unclear when Manchin might do so, but it would likely not be until after Byrd’s funeral Friday.

Democratic aides confirmed that leaders are also in touch with Iowa Republican Chuck Grassley, who voted with most Republicans to filibuster the bill but supported the Senate version on final passage. A Grassley spokeswoman said he was still evaluating the conference report. Other Republicans on the Democrats’ target list include Sens. George Voinovich (Ohio) and Dick Lugar (Ind.).

Feingold has already announced his opposition to the conference report. But Dodd, who did not mention Feingold by name, indicated he believes an early end to the 2008 bailout fund could be an enticement for some Senators who opposed the fund from the beginning, as Feingold did.

Meanwhile, Senate Republicans came under increased pressure to block the conference report, even with the changes conferees made Tuesday evening.

Sen. Bob Corker (R-Tenn.) said Republican leaders and rank-and-file Members urged their colleagues to hold off on making any deals with Dodd or Democrats on the bill this week.

“I do think that if we could hang together for another couple of weeks that we could end up with a real bipartisan bill,” Corker said, noting that sentiment was expressed by several Members at the party’s regular Tuesday luncheon.

He added that Republicans should take advantage of the troubles Democrats are having in getting a filibuster-proof majority for the measure. “They’re running into the issues due to the route they’ve taken,” Corker said, “which is to try to produce a partisan bill. … I hope they have trouble and I hope we end up in July trying to cause this to be a bill that will stand the test of time. This one will not do it and it can be fixed and they know how to fix it.”

But Snowe and Collins indicated they were moving forward despite the pressure to bide their time.

“I am working with Sen. Dodd to see if there’s a way for us to move away from the new tax, and I believe we’re making progress in that area,” Collins said.

Frank said he was surprised by Senate GOP objections to the $19 billion assessment on banks and hedge funds, saying he thought it made sense to force big banks to “pay for the cost of the regulation.”

“I’m puzzled that my Republican friends want to come to the rescue of large financial institutions,” Frank said. “I was puzzled but that’s the vote situation.”

Frank also said he was “disappointed” Feingold was opposed to the measure.

“I have no idea what he thinks he’s accomplishing by strengthening the Republicans’ hand,” he said. “Maybe he will be happy now that there’s no … hedge fund fee because that’s what he helped accomplish.”

Still, Frank said Dodd was “confident” he has 60 votes locked down for the measure.

A House Democratic leadership aide said leaders were confident that the conference report — with the changes that Dodd negotiated — would garner enough votes to clear their chamber.

“We believe our members will be OK,” the aide said. “We are for what can get them 60.”

House Democrats had few votes to spare in December when they passed their version of the bill. Any assurance that the Senate will quickly clear the conference report once the House acts likely would help leaders convince their Members to stay in line.

“We will have the votes when we go to the floor,” said Nadeam Elshami, a spokesman for Speaker Nancy Pelosi (D-Calif.).