Key Republican questions Obama's strategy on ground troops in Syria

House Homeland Security Committee Chairman Mike McCaul said Sunday that the Obama administration is being "unwise" by not looking for other countries who might send ground troops into Syria to fight the Islamic State of Iraq and Syria (ISIS, also known as ISIL.)

"I do agree with the sort of strategy that we want the Sunni moderates, the Arabs, to fight the Sunni extremists. I don't think we want to put our conventional combat troops in the middle of a lot of this," McCaul said in an interview on CBS' "Face the Nation." But recalling a meeting two days ago in which Jordanian Prince Feisal Bin Al-Hussein said he is ready to send his own troops into Syria to fight ISIS, McCaul said, "I don't know why we wouldn't consider that option."

He also suggested Egypt's military could be useful in fighting the militants.

In a interview on "Face the Nation" Sunday, Secretary of State John Kerry said that while the U.S. has received some offers of ground troops from other nations, "we are not looking for that at this moment."

That was not McCaul's only criticism of the White House. Speaking more broadly about Mr. Obama's handling of the crisis, he said, "ISIS does not fit in this president's narrative."

"His narrative was, 'I am the president to end these wars' and so now when he looks at his legacy he can't get his head wrapped around the idea of what ISIS is and how to defeat it and what an imminent urgent threat that it really is," McCaul said. "Now its catch-up time, and its catch-up time trying to get a coalition together, and a strategy together."

Mr. Obama has said he has the authority he needs to carry out airstrikes in Syria and is only seeking additional authorization from Congress to further arm and train the moderate rebels there. But McCaul said he believes Congress should authorize the airstrikes as well.

"I think the American people need to weigh in with their support and I do think while we're just going to vote on a limited authorization with respect to raining and vetting these moderate Syrian forces...it's important for congress to authorize these airstrikes, particularly into Syria," McCaul said. "We cant cut the head of the snake off unless we go to where it is and the head of the snake is in Syria."

Not all lawmakers, even Democrats, are going to be supportive of the president's proposal to arm the rebels, however. In an separate interview on "Face the Nation," Sen. Kirsten Gillibrand, D-N.Y., said she doesn't think that is a good strategy.

"I don't think arming the rebels in this instance is necessarily going to be productive. We spent years training the Iraqi forces, the Iraqi police forces, the Iraqi military forces. And ISIS was able to cut through them like butter," she said. "But there are things that he is asking our support for that I do support. I do think this multilateral engagement is wise. It has to be participations by Sunnis, by Muslims, by Arabs all across the Middle East. And if he continues to form a coalition to deal with this serious terrorist threat, that is the right approach."