(CBS News) A handshake agreement between the United States and Russia to identify Syria's chemical weapons, place them under international control and ultimately dismantle them was "the only way to solve" the the immediate crisis of chemical weapons use in Syria's ongoing civil war, Sen. Bob Corker, R-Tenn., said Sunday on "Face the Nation."
On the other hand, Corker - the top Republican on the Senate Foreign Relations Committee - said, "I think all of us have to approach this with a healthy and strong degree of skepticism. The fact that it's not only what is said in these agreements, but what is not said, or what is said privately.
"...The threat of force from a multilateral standpoint is still very much in Russian hands," he went on. "That's the most important element, is the veto piece. So in many ways our credibility in the region, and certainly relative to the chemical warfare, is very much driven by Russia, which has its hands firmly on the steering wheel."
It does mark "significant progress," agreed Sen. Carl Levin, D-Mich., the chairman of the Armed Services Committee, that Russia was willing to go in on a tentative deal to secure and destroy Syria's chemical weapon stockpile. Still, it "will not be fully implemented, I'm afraid, without a continuing threat" of possible military action from the United States, he added.
A longtime ally of Syria, Russia "can force" President Bashar Assad, who the United States has alleged used the chemical weapons against his own people, "to do what Russia wants Assad to do," Levin continued. "It is the weapons supplier for Assad; it has been deeply involved in one of the very few countries that have supported Assad."
Corker, meanwhile, said he has expressed to Secretary of State John Kerry worry that the agreement will set back U.S. support for the Syrian opposition.
"We certainly have not done what we need to do" in terms of providing aid to the rebels fighting to overthrow Assad, he said. "It has hurt our credibility, certainly, on the ground. ... But the way to counter that, I think, is to much more strongly equip and train the opposition there on the ground."
The United States is "not going to agree to" Syria's attempt to stifle support to the opposition as terms of its compliance with the U.S.-Russia deal, Levin said.
"We have supported the opposition, I agree, not sufficiently," he said. "I have always called for increasing the military pressure on Assad by supporting the opposition, and I think we should do that and I think we now have some indication from the administration recently that there will be ways found to provide greater military support, hopefully, including anti-tank weapons for the opposition."
There are "going to be mistakes," Corker conceded, in determining who among the opposition should be armed - "some people are going to get arms that should not be getting arms." But, he went on, "I think we know more than we led on publicly about which groups to support and which not - we need to do much more to help them."