"tough going" for the administration, at least in the House, Rep. Tom Cole,
"I think it's going to be a very tough sell," said Cole, often a key crossover Republican in White House compromises.
Cole said he was "leaning no" on approving any use of force against Syria.
Rep. Peter King, R-N.Y., a former Homeland Security Committee chairman, went so far as to say the measure would likely lose if a vote were held in the House now, because of the body's "isolationist wing."
Cole added he expected Obama would be bound by the House and Senate votes and wouldn't authorize a strike if Congress voted no.
Lawmakers said the biggest stumbling block was the fear a limited strike would do little to deter Assad but would clearly draw the United States deeper into Syria's civil war.
"I don't think there's a lot of doubt that the regime undertook this attack," said House Intelligence Committee member Jim Himes, D-Conn. "There's a great deal of skepticism that a limited strike is likely to be effective."
Both the House and Senate are expected to debate and vote on the measure shortly after they return from recess Sept. 9.
While a number of lawmakers who spoke Sunday said they were reticent about supporting military action, Senate Majority Leader Harry Reid of Nevada and House Democratic leader Nancy Pelosi of California issued statements strongly supporting it.
Senior aides told The Wall Street Journal the Democratic leaders would work hard to build support within their party.
Sunday, McCain, a key Republican Obama ally in the use of force, said he would not support "isolated military strikes in Syria" that were not part of a broader strategy to shift the momentum on the battlefield to the rebels.
He also questioned the administration's decision to seek congressional approval before acting, pointing to Obama's declaration months ago a chemical attack would be a "red line" that, if crossed, would be met with military force.
"He didn't say that it's a red line and, by the way, I'm going to have to seek the approval of Congress," McCain said on CBS' "Face the Nation."
Before Sunday's congressional briefing, Secretary of State John Kerry said on five morning talk shows he expected Congress would ultimately back the president's plan for military action.
"I do not believe the Congress of the United States will turn its back on this moment," he said on "Meet the Press."
"I think the interests that we have with respect to potential future confrontation, hopefully not, but the challenge of Iran, the challenges of the region, the challenge of standing up for and standing beside our ally Israel, helping to shore up Jordan -- all of these things are very, very powerful interest[s]. And I believe Congress will pass it."
When asked if Obama would act regardless of what Congress votes, Kerry said, "I said that the president has the authority to act, but the Congress is going to do what's right here."
Kerry said on the talk shows the administration now had evidence the chemical weapons allegedly used in the attack contained sarin. He said blood and hair samples from first responders who helped attack victims tested positive for the nerve agent.
Kerry later reached Arab diplomats to garner support ahead of an Arab League meeting in Cairo Sunday night.
The league later said in a statement it held the Assad regime "fully responsible" for the chemical weapons attack and asked the United Nations and the international community "to take the necessary measures against those who committed this crime."
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