Washington (CNN) -- President Obama and Republican and Democratic leaders engaged in a spirited but civil debate at a health care summit Thursday, finding agreement on some issues but appearing to find little common ground on how to move forward in a bipartisan way.





"I don't know, frankly, whether we can close that gap," said President Obama as the day-long meeting closed. If agreement is not reached, he said, there will be "a lot of arguments about procedures in Congress about moving forward," an apparent reference to using a parliamentary shortcut under which a health care bill could be passed with a simple majority instead of the 60-vote supermajority the body requires to overcome the filibuster which Republicans have threatened to use.





"My hope had been there might be enough areas of overlap to realistically think about moving forward without a situation in which everyone just goes to their respective corners and this ends up being a political fight," he said.





"Frankly, I was discourage by the outcome," Senate GOP leader Mitch McConnell of Kentucky, told reporters after the meeting. He urged the Democrats to "start over and go step by step and target the areas of possible agreement that we discussed in the meeting today."





Sen. John Boehner, R-Ohio, sounded equally unenthusiastic. "I think the American people want us to work together on common steps to make our current system work better," he said. "We can't do it within the framework of a 2,700-page bill."





Live updates from the health care summit





"The president let everybody talk and talk and talk," said Senate Majority Leader Harry Reid, who called Obama "the most patient man in the world."





Though there were areas of agreement, he said, "every Republican used the same talking points." He, too, appeared to raise the specter of attempting to move forward through the parliamentary shortcut, known as reconciliation.





"It's time we do something and we're going to do it," the Nevada Democrat said.





House Speaker Nancy Pelosi said she was "not overly optimistic" that the Democrats would be able to attract Republican votes for the health care bill.





Obama said in opening remarks that "it is absolutely critical to begin now moving on what is one of the biggest drags on the economy."





The situation affects not just people without health insurance, but also those who have it, he said.





"The problem is not getting better," he said. "It is getting worse."





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Obama called on Republican and Democratic leaders at the much-publicized summit to "not focus on where we differ, but focus on where we agree."





The differences were evident, though, in what each side believes should happen next.





Republican Sen. Lamar Alexander, who made the opening remarks for his party, said Democrats should scrap existing bills passed by the House and Senate and start over on new legislation.  Watch what areas Democrats and Republicans can agree on





That's not going to happen, Democrats answered, saying Americans cannot wait.





"For them, they don't have time for us to start over," House Speaker Nancy Pelosi said.





Jon Kyl, the Senate Republican Whip, pointed out that a major philosophical difference between the two sides is who should be in charge of the health care system -- the government or private industry.





"There's so much in the bills you have supported that puts so much control in Washington," Kyl said to Obama.





House Republican Whip Eric Cantor also highlighted that concern, pointing out that Republicans are nearly unanimous in their opposition to the bills.





"There is a reason we voted no," Cantor said to Obama. "It does have to do with the philosophical differences you pointed out. It also has to do with our fear that Washington can define what are essential health benefits."





Democratic Sen. Tom Harkin made an impassioned plea for passage of health care reform, saying the current system discriminates against
Who urged Democrats to scrap the health care bill? Who said the health care system discriminates?
Republican Sen. Lamar Alexander, Democratic Sen. Tom Harkin
question: Who urged Democrats to scrap the health care bill?, answer: Republican Sen. Lamar Alexander, | question: Who said the health care system discriminates?, answer: Democratic Sen. Tom Harkin