President Barack Obama’s request for speedy congressional backing of a military strike in Syria advanced in the Senate on Wednesday, hours after the President left open the possibility he would order retaliation for a deadly chemical weapons attack even if Congress withheld its approval.

A resolution cleared the Senate Foreign Relations Committee on a 10-7 vote after last-minute alterations to support “decisive changes to the present military balance of power” in Syria’s civil war. It would rule out U.S. combat operations on the ground.

The measure is expected to reach the Senate floor next week, though the timetable for a vote is uncertain.

The support seen in the Senate will be harder to find in the Republican-controlled House of Representatives. Secretary of State John Kerry and other top administration officials made the case for action on Wednesday during a heated House hearing.

At the House hearing, Mr. Kerry said Assad had used chemical weapons 11 times, including once last spring. At that time, he said, Mr. Obama did not have a “compelling” enough case to push for a U.S. military response.

Asked about international support for Mr. Obama’s threatened military strike, Mr. Kerry said Arab nations have offered to pay the cost of any U.S. military action. He was not specific but said the offers have been “quite significant, very significant.”

“Some of them have said that if the United States is prepared to go do the whole thing the way we’ve done it previously in other places, they'll carry that cost. That's how dedicated they are to this.”

The top American military commander has said that the U.S. is ready for any retaliatory action from Syria.

Testifying before a Congressional committee on Syria, General Martin Dempsey, Chairman of the Joint Chiefs of Staff, conceded that the proposed military action is not about eliminating chemical weapons and it is not possible to do so. “This isn’t about eliminating chemical weapons. That’s not possible given the number and the distribution of them. It’s about convincing the Assad regime that it’s unacceptable for them to use them, and that’s the limit of this military operation,” General Dempsey told lawmakers in response to a question.

“We’re postured for the possibility of retaliation, and I can assure you that our regional partners are, as well,” he said

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