(Joshua Roberts/BLOOMBERG NEWS)

But there was some friction in the East Room of the White House, several House Democrats said after the meeting, when members pressed Obama for greater clarity regarding the slated drawdown of U.S. troops from Afghanistan next month.

Obama invited the House Democrats to the White House one day after holding a similar meeting with House Republicans. He told members of his party that he believes revenue increases must be part of a deficit-reduction deal, and he charged that the budget plan drafted by Rep. Paul Ryan (R-Wis.) would raise health care costs for seniors by more than $6,000, according to a House Democratic source.

House Republicans have come under fire from Democrats for their proposed Medicare changes. They contend that their budget plan would preserve Medicare by privatizing the entitlement program for future seniors; they also argue that Democrats have not put forth a plan that would prevent Medicare from becoming insolvent by 2024.

Congressional leaders and the White House are working on a plan to reduce the long-term deficit in exchange for a raise in the country’s $14.3 trillion debt limit. House Democrats told Obama on Thursday that they would support a deal that included both tax increases and spending cuts, so long as those cuts were not targeted at seniors and the middle class.

The meeting came the same day as the Moody’s credit rating agency warned that it may downgrade the United States' credit rating if Congress and the White House fail to make progress on a deficit-reduction deal in the next several weeks. The Moody’s report echoed a similar warning issued by Standard & Poor’s in April.

The debt-limit debate was the main focus of Thursday’s meeting, but U.S. military involvement abroad also came up at the gathering.

One of the leading Democratic opponents of the war in Afghanistan exited the White House disappointed with Obama’s lack of clarity on what he plans to do next month, when a drawdown of troops from Afghanistan is slated to begin.

“I told him that if it’s just a token drawdown, I think people will be pretty outraged by that. The American people want an end to this war,” Rep. Jim McGovern (D-Mass.) said afterward. McGovern, the author of a plan to set a firm timeline for withdraw, added that he felt Obama had evaded the specifics of how many troops would begin to come home.

“I don’t feel we got an assurance that there would be a substantial and significant drawdown of American forces in July,” McGovern said. “He didn’t tell us what it would be, but I didn’t get the assurance that I was hoping to get.”

Other Democrats said that McGovern received a strong applause from rank-and-file Democrats for pushing the president on the issue.

McGovern has received growing support for his amendment to force a quicker withdrawal. Last year, the plan won 162 votes; by last week, it nearly passed, receiving 204 votes. He said Thursday that there is little time left for the current policy on Capitol Hill.

“The American people are ahead of Congress and they’re ahead of the administration on this issue. ... They’re getting tired of endless wars,” he said.

The House is set to vote Friday on two resolutions related to U.S. military operations in Libya, which are on their 75th day. Just as the war in Afghanistan has drawn more vocal opposition in recent months, the U.S. involvement in Libya has been criticized by liberal House members such as Rep. Dennis Kucinich (D-Ohio) as well as conservatives such as Rep. Allen West (R-Fla.).

Kucinich said that he had wanted to ask Obama a question on Libya at Thursday’s meeting, but that there wasn’t enough time for him to do so.

Earlier Thursday, House Speaker John Boehner (R-Ohio) said that members of Congress are increasingly voicing their concerns about U.S. involvement abroad in part because Obama has failed to clarify to Congress and the public the goal of U.S. operations.

“The doubts that our members have, quite frankly, are reflected — they’re reflecting what they’re hearingo from their constituents,” Boehner said at a news conference. “I think the president has a role to play here and the president really does need to step up and help the American people understand why these missions are vital to the national security interest of our country.”