Rep. Mike Rogers, chairman of the House Intelligence Committee, wants to see Congress approve the president's proposal, but he also argued the administration has fumbled the ball when it comes to wooing Capitol Hill.
"I think it's very clear he's lost support in the last week," the Michigan Republican said on CBS's "Face the Nation."
Rogers' comments on Sunday marked a stark contrast to the optimism he expressed a week ago, when he said on CNN he believed Congress would "rise to the occasion" and pass the president's proposal.
But Rogers now says the Obama administration has done an "awful job" in making its case, saying administration officials are not focusing enough on how Syria's ties with Iran could be potentially damaging to the United States.
He also criticized the president for traveling to the G20 summit in Russia last week without calling Congress back from recess to have a national security debate over whether to take military action in Syria.
"The way it happened was mystifying," Rogers said, referring to the president's proposal August 31 for congressional authorization. "He announced it and then left."
Sen. Chris Coons, a Democrat from Delaware and a member of the Senate Foreign Relations Committee, said Sunday he would not have supported the president's original authorization language, but after the committee redrafted the authorization to make it more narrow, he's now in favor of taking action.
"I do think that we know what the consequences of inaction will be, that we know that Bashar al-Assad, one of the worst dictators who has used some of the worst weapons in American -- in world history will continue to use cluster bombs and scud missiles and chemical weapons to massacre thousands of his own civilians," Coons said on State of the Union.
The Senate Intelligence Committee posted on its website Saturday night troubling videos of people dying in the aftermath of the August 21 chemical attack in a Damascus suburb. The same videos were shown in a classified setting last week to members of the Senate and were slated to be played Monday at a briefing for House members.
Rep. Justin Amash, R-Michigan, said the videos, which were first shown to the public by CNN earlier Saturday, are "horrific" but don't "determine whether we should go to war."
"I've talked to my constituents, and they are overwhelmingly opposed to going to war," he told CNN. "I've been to the classified briefings, I know what the evidence is, and I think the case is not that strong right now."
Speaking on "Fox News Sunday," McDonough argued "it's too early to come to any conclusion" about how Congress will vote.
The White House chief of staff, who took part in a series of TV interviews Sunday, said on CNN he has spoken with dozens of members of Congress and "not a single one rebuts or refutes the intelligence and the evidence."
The question they face, he said, is whether Syria's regime should "be held to account for carrying out this activity."
"If members of Congress want to answer that question, to say that there should be consequences for this action, then they're going to have to vote yes for the authorization," he said.
Many of the undecided lawmakers may wait until Obama makes his case the American people Tuesday night at 9 p.m. ET in a speech from the White House.
Rep. Sander Levin, D-Michigan, said Friday the president needs "to talk to the public, and lay out the facts as fully as he can." Levin has said he plans to vote "yes" on the authorization.
"This is gonna be a fireside chat, somewhat like it was in the '30s. I wasn't old enough to know, but one has to remember how difficult it was for President Roosevelt in World War II," Levin said Friday after a joint closed briefing for members on Capitol Hill.
Sen. Rand Paul, R-Kentucky, said Sunday he was still weighing his options for stalling a vote in the full Senate on the use of force resolution. The Kentucky Republican said a filibuster could only delay a vote but wouldn't "put off a vote forever."
Instead, he said, he'd demand that any vote taken by Congress be binding, meaning that the president would be barred from striking Syria without congressional approval.
"The president cannot, if we vote him down, decide to go to war anyway. That's the way I interpret the Constitution," Paul said on "Fox News Sunday."
Rep. Elijah Cummings, D-Maryland, told reporters he would be surprised if Obama went against Congress if they said "no."
"There are two sides to this. When he asked for Congress' consent, he was also asking for the American people's consent," he said. "But the flip side of that is if you don't get that consent, I think that it would be appropriate not to move forward."