Senate leaders on Tuesday worked to reassure a wobbly Wall Street that a bailout bill will be finished this week, mindful of the potential political fallout from Monday’s failed House vote.

The push by Majority Leader Harry Reid (D-Nev.), Minority Leader Mitch McConnell (R-Ky.) and senior GOP leaders like Minority Whip Jon Kyl (Ariz.) and senior Senate Banking Committee members Judd Gregg (N.H.) and Bob Bennett (Utah) is coming through floor speeches, statements and comments to reporters.

“I too want to reassure the American people that we intend to pass this legislation this week,” said McConnell. “We will pass it on a broad bipartisan basis, both sides cooperating to prevent this financial crisis from persisting. We know what we have to do, we know we have to do it quickly, and we know time is not an ally for millions of Americans.”

The Senate is closed Tuesday for formal votes, but the chamber is open and both McConnell and Reid are at the Capitol. Both parties are negotiating on a path forward after Monday’s 205-228 House vote against the Bush administration’s $700 billion plan to shore up the U.S. financial markets. The vote trigged a 777-point drop in the Dow Jones Industrial Average, but markets on Tuesday regained some of their steep losses.

A total of 133 House Republicans opposed the bill, along with 95 House Democrats. Although controversial legislation usually faces longer odds in the Senate, the so-called bailout bill had been expected to pass through the upper chamber by a wide margin.

Reid said Democratic presidential nominee Barack Obama (D-Ill.) has spoken with President Bush, and Reid himself has spoken with White House Chief of Staff Josh Bolten about the situation. Reid’s office also said the majority leader is considering a letter to Bush to emphasize the Senate’s readiness to take up the issue, and leading Democrats like Hillary Rodham Clinton (N.Y.) and John Kerry (Mass.) were issuing statements and holding conference calls to promise quick bipartisan action.

“We cannot let the perfect be the enemy of the good, or in this case the enemy of what’s necessary,” Clinton said. “We have to go back and, in a bipartisan fashion, face up to the difficult decisions ahead of us.”

GOP leaders seemed to sense the brunt of the effort was on their shoulders, given that more House Republicans than Democrats voted against Monday’s bill, as well as the fact that the bill was based on a Sept. 18 proposal by the Bush administration. They also told reporters they were optimistic that the solution would be quick and bipartisan.

“There is a will to get this done, and get this done quickly, and the White House is in the same mode,” said Kyl. “You’d think that that much will to get that done should ultimately prevail. I think we’re on a pretty good track right now. Everybody is working in a constructive way. Sometimes when you have an event like occurred in the House, it focuses the mind, and I think everybody is very focused now.”

Kyl confirmed that Senate GOP leaders have been in touch with their House counterparts, but sidestepped a question about whether GOP presidential nominee Sen. John McCain (Ariz.) should return to Washington. Kyl said only that he was focused on making sure no one single vote would be necessary for passage.

Although the Constitution requires the bailout bill to originate in the House because it involves taxation issues, the Senate could skirt that by taking up a House bill already pending in the upper chamber and use it as the vehicle for a bailout bill. It was unclear how much traction was behind the idea, but both Democrats and Republicans confirmed it was being discussed.

“Anything that’s within the realm of the rules is within the realm of possibility,” said Bennett.

Senate Banking Committee Chairman Chris Dodd (D-Conn.) had quashed that idea in remarks to reporters on Monday, saying such a strategy would “compound” the already complicated situation.

Veteran Republican Kit Bond (Mo.) said he could understand lawmakers who are philosophically opposed to government intervention in the financial markets. However, Bond added that “with or without this bill, taxpayers are already on the hook.”