A Wednesday briefing by Army Gen. David Petraeus did not appear to quell concerns of House Democrats who are set to pass a veto-ready supplemental war spending bill that includes a timeline for withdrawal.

But the top commander in Iraq did warn lawmakers that their volatile rhetoric is being heard by the enemy.

"One thing that he reminded us was, this is a test of wills and he admonished us, reminded us that what we say to the world, to our adversaries and our allies, is listened to by the other side," said Rep. Duncan Hunter, R-Calif.

Hunter said Petraeus "didn't try to sugarcoat the issues and the problems" that American forces face in Iraq, but noted that comments like that by Senate Majority Leader Harry Reid, who last week said the war is lost, provide incentive for U.S. adversaries.

"It must come as a shock to Al Qaeda leaders to have an aide come into their safe house and tell them that Senator Reid has declared that, in fact, they are winning and the war is lost," Hunter said. "I think it's highly irresponsible for the leader of the U.S. Senate to have said that and, just speaking for myself as the ranking Republican on the Armed Services Committee, I think that the leader of the Senate should step down from that position."

Wednesday's briefing by the head of Multinational Forces in Iraq was intended to provide new insights about the long-term viability of the security plan, but appeared only to harden partisan positions on the war.

"Our troops are mired in a civil war with no clear enemy and no clear strategy for success," House Majority Leader Steny Hoyer, D-Md., said after leaving the briefing room. "This briefing reinforced our view that the solution in Iraq is a political solution."

Petraeus briefed more than 200 members just hours before the House vote on the bill that requires combat troop withdrawals to begin this year and seeks removal of virtually all combat forces by April of next year. He then briefed Senate members, who also packed the meeting room. The Senate is expected to vote on the measure on Thursday.

After the Senate briefing, Minority Leader Mitch McConnell agreed with Hunter's assessment about the message conveyed by a timetable, and said the bill should not have a "surrender date."

"We don't need to send a memo to our enemies about when we intend to quit. It's highly demoralizing to our troops and unsettling to our allies," McConnell said.

But Sen. Carl Levin, D-Mich., said notice of Congress' plan is being used by administration officials, including the secretaries of defense and state to encourage political actions in Iraq that may otherwise not get done.

"Each one of them has used this debate as a way of putting pressure on the Iraqi leader," Levin said.

Joined by Deputy Secretary of State John Negroponte, Deputy Secretary of Defense Gordon England and Joint Chiefs of Staff Chairman Peter Pace, it was Petraeus' first appearance on Capitol Hill since becoming the top commander in Iraq. His assessment on the latest military efforts to lessen sectarian and Al Qaeda-sponsored violence in Iraq was given behind closed doors and included a question-and-answer session.

It seemed unlikely the briefing would help shape the outcome of what is expected to be a close House vote Wednesday night on the troop funding bill. The earlier House version of the bill passed with 218 votes, the bare minimum needed for passage.

The emergency war supplemental bill that emerged from a conference committee between House and Senate Democrats on Monday includes a mandatory troop withdrawal schedule to start removing combat forces as early as July and no later than October. The bill also includes a goal of removing virtually all combat forces from Iraq by the end of March next year.

Leaving the briefing, Rep. James Clyburn, D-S.C., the House majority whip, said the Democratic plan provided an "exit strategy that the president ought to be pleased to receive."

Democrats are skeptical of the surge and are trying change to course in Iraq, saying the violence in Iraq is part of a civil war and represents no threat to the United States. Hoyer, however, acknowledged that the departure of troops may not end the threat to the United States.

"General Petraeus made it very clear that sectarian violence was the most disruptive element," Hoyer said. "Al Qaeda obviously is a very significant presence at this point in time. As you know in the bill we specifically provide and reserve the right for troops to confront Al Qaeda."

All lawmakers were invited to the general's briefing, but House Speaker Nancy Pelosi did not attend nor did Rep. John Murtha, D-Pa., chairman of the committee responsible for defense appropriations.

Pelosi's staff cited a scheduling conflict for her absence. However, she and Murtha spoke by phone with Petraeus for 30 minutes on Tuesday, which she said was sufficient.

"I appreciated his report and his responses to my questions on security and political issues in Iraq," Pelosi said in a statement about her and Petraeus' phone conversation. "We share a conviction that the war in Iraq will not be resolved militarily, and I look forward to future reports from him on the effects of President Bush’s escalation plan."

House speakers rarely attend members-only military briefings, but Republicans took no time in criticizing the speaker for her absence. Minority Leader John Boehner of Ohio called Pelosi's decision "shameful." Rep. Joe Wilson, R-S.C., called it "insulting and disrespectful."

"While Speaker Pelosi was able to jet-set around the globe to meet with Syrian leaders, she finds it inconvenient to meet with the U.S. commander in Iraq during his brief visit to Washington," Wilson said.

The Democrats' war funding bill requires monthly assessments from Petraeus on military progress in Iraq as the surge continues. Democrats have described these updates as crucial to Congress' ability to measure success in Iraq. Pelosi's absence could be seen by some as undercutting the importance of these monthly briefings.

FOX News' Major Garrett contributed to this report.