(CNN) -- Sens. John McCain and Barack Obama left a White House meeting, described as at times "contentious," with no apparent financial bailout deal worked out.
Obama, appearing on CNN's "The Situation Room" after the meeting, said there "has to be a sense of urgency on the part of everybody. ... We've got to move rapidly."
Obama said that there will be a deal eventually but that there is still work to do, including reaching a consensus among Bush, Treasury Secretary Henry Paulson and House Republicans.
McCain told ABC News on Thursday night that Republicans "have legit concerns. Some of those have already been satisfied, such as accountability and oversight board and CEO executive pay. Members are aware of the crisis situation that we are in."
But, McCain said, "They do have concerns, which I think when you're talking about 700 billion to a trillion dollars, that need to be addressed."
Obama, who will spend Thursday night in Washington, once again railed against infusing presidential politics into the negotiations over the $700 billion economic bailout. McCain's campaign said he will also stay in the Washington area for the night.
"One of the concerns I've had over the last several days is that when you start injecting presidential politics into delicate negotiations," Obama said, "then you can actually create more problems rather than less." Watch more of Obama's comments »
Democratic sources said that House Minority Leader John Boehner threw a wrench into the meeting when he brought up issues from conservative Republicans that negotiators thought had been settled.
But a House leadership aide said that there had been no bipartisan negotiations with House Republicans. The aide said Rep. Spencer Bachus, who had been meeting with Sen. Chris Dodd and Rep. Barney Frank, heads of the Senate and House banking committees, had no authority to speak for them.
In a statement before the meeting, Bachus said that he had made it clear in the meeting that "I was not authorized by my colleagues to make any agreement on behalf of House Republicans."
Boehner said that he needed more time to get agreement from House Republicans, a senior administration official said.
Obama asked whether the House Republicans' proposals fit in with the four principles that the leadership had agreed on, but Boehner couldn't answer that, a Democratic source said.
Multiple sources said McCain didn't say much. Two Democratic leadership aides said he didn't speak until 43 minutes into the meeting.
When asked whether Friday's debate will go on if McCain doesn't show up, Obama said: "I hope he does."
McCain also told ABC News that he was "very hopeful that we can [attend the debate.] I believe that it's very possible that we'll get an agreement so that I have time to fly to Mississippi."
CNN has learned that the University of Mississippi -- site of the first presidential debate -- has been told by the Presidential Debate Commission to continue preparing for the event.
Both McCain and Obama advance teams were seen on stage going through sound and video checks from their candidates' respective podiums.
In Washington, White House press secretary Dana Perino released a statement saying, "The president appreciates the bipartisan members of the congressional leadership and the two presidential candidates coming to the White House today to discuss how to finalize the financial rescue package. There is a clear sense of urgency and agreement on the need to stabilize the financial markets, and prevent a massive financial crisis from affecting everybody in America."
The statement went on to say that the group will continue to work on a deal.
But according to Sen. Richard Shelby, R-Alabama, who attended the meeting, "we will not have a deal." Watch iReporters react to the bailout negotiations »
The meeting included many key players: Bush flanked at the table by Senate Majority Leader Harry Reid and House Speaker Nancy Pelosi, Obama and McCain on opposite ends of the table, Boehner and Senate Minority Leader Mitch McConnell also between the two presidential candidates and Vice President Dick Cheney across from Bush.
According to several Republican aides, there is still major opposition to the "agreement on fundamental principles."
The fact that House Republicans are still not coming on board poses a major obstacle for any kind of deal. Pelosi and other House Democratic leaders have repeatedly said that this is Bush's bill and that he and other GOP leaders need to get Republicans to support it.
McCain, who announced Wednesday that he was suspending his presidential campaign until a bailout plan was worked out, met with some Republican House members to try to bring more of them on board to back the agreement, according to a source in the room and one who was briefed on the meeting.
The gist of the meeting, according to sources, was that these members "aren't there yet" on the plan the Senate Banking Committee worked out and say there needs to be greater protection for taxpayers.
One Republican aide said that "not much has changed in the last 24 to 48 hours. I think it has to be pretty radically altered for House Republicans to support it."
This aide stressed, "at the end of the day, these members represent the people who sent them here, and the people who sent them here are so overwhelmingly opposed to this."
This aide said the calls coming into GOP offices are 90 to 1 against the plan.
Boehner, R-Ohio, has tapped a group of House Republicans to develop alternative ideas.
Earlier, Boehner released a statement that said, "I am encouraged by the bipartisan progress being made toward an economic package that protects the interests of families, seniors, small businesses, and all taxpayers."
It's unclear whether McCain agreed with this approach, but one aide said he put the principles "in his satchel to take over to the White House."
Republicans recognize that there is pressure building to get something done before the end of the week. "There sort of a tacit understanding among everyone that it has to happen before Monday," a third GOP aide said.
Obama turned down McCain's suggestion that they both suspend their campaigns to focus on securing a deal on a bailout plan. He also passed on McCain's suggestion that they postpone Friday night's first presidential debate in Oxford, Mississippi.
Democrats fear that McCain will take credit for bringing reluctant Republicans around to agreeing with a bailout plan in order to bolster his argument that he would be a better leader in crises than Obama.
"The Democrats, of course, are very afraid that McCain is going to swoop into these delicate negotiations on Capitol Hill at the last minute and when they reach an agreement, he's going to claim credit for having brought those negotiations to a successful conclusion," CNN senior political researcher Alan Silverleib said.
A McCain source insists that the Arizona senator is aware of the politics involved and recognizes that Democrats -- and even some Republicans -- are wary of having it appear that McCain is brokering a deal.
CNN's Dana Bash, Peter Hamby, Ed Hornick, Suzanne Malveaux and Deirdre Walsh contributed to this report.