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But U.S. lawmakers from both sides of the aisle remain skeptical.

Sen. Tom Udall, New Mexico Democrat, said even targeted strikes constitute an act of war.

“I’m very disappointed that the administration has given up. They have given up on the United Nations and on rallying the world,” Mr. Udall said Sunday on NBC’s “Meet the Press.” “I think what we’re talking about is moving much too rapidly down the warpath and not trying to find a political solution through the international community.”

Sen. Ted Cruz, Texas Republican, appearing on ABC’s “This Week,” said, “One, I think the administration is proceeding with the wrong objective, and two, because they have no viable plan for success.”

Mr. Cruz suggested alternatives, including cutting off aid to Iraq unless it revokes air rights to Iran, a key Syrian ally, and forcing a vote in the United Nations Security Council to make Russia and China veto it publicly.

“I don’t think that’s the job of our military to be defending amorphous international norms,” Mr. Cruz said.

Sen. Rand Paul, Kentucky Republican, said Congress’ decision on whether to strike should be binding on Mr. Obama, who has suggested he may order a strike on Syria with or without congressional permission.

“He has already been proven to go above the law in several instances,” Mr. Paul said on Fox, citing nominations during recess as one example. “Whether you impeach someone is a different issue and a very big one.”

A top House Democrat said that while the White House may have the legal authority to launch an attack without Congress, going over the heads of lawmakers wouldn’t be right.

“I think while he has the constitutional authority, I think morally he will have lost the authority to move forward,” Rep. Xavier Becerra of California, the House Democratic Caucus chairman, said on C-SPAN’s “Newsmakers” program.

Rep. Elijah E. Cummings, a Maryland Democrat from a pro-Obama district, said it’s “possible” that he would support the president under a more limited resolution being drafted by the House.

“I want to support the president. I believe in him. And I believe that if the president, being a president that came in and campaigned on taking us out of war says that, you know, I think we need to do this. I want to make sure I understand what he is seeing,” he said on CBS’ “Face the Nation.”

It’s not just Democrats supporting limited strikes. Rep. Mike Rogers, Michigan Republican and chairman of the House Permanent Select Committee on Intelligence, said he wants Congress to approve a resolution. But the broken relationship between Congress and the president is part of the problem in getting the votes needed for a resolution, he said.

“They don’t have strong relationships in Congress — today that’s a huge problem for them — and candidly have done an awful job explaining to the American people what is in our national security, what is the national United States interests in any level of engagement in a place like Syria,” he said on CBS’ “Face the Nation.” “It is a confusing mess, up to this point.”