Congressional leaders remain insistent that any deal with Russia regarding Syria's chemical weapons can't compromise the U.S.'s ability to arm opponents of Syrian Prime Minister Bashar Assad.

"We are not going to agree to that," said Sen. Carl Levin, D-Mich., chairman of the Armed Services Committee, on CBS's "Face the Nation."

There's bipartisan accord that the administration must do more to get weapons into the hands of moderates fighting the Assad regime, even as the U.S. seeks to peacefully eliminate Syria's stockpile of chemical weapons.

"Dramatically more assisting the vetted, moderate Syrian opposition is, I think, incredibly important," Sen. Bob Menendez, D-N.J. told David Gregory on NBC's "Meet the Press."

Last week, reports surfaced that covert CIA efforts allowed the U.S. to get some weapons to rebel fighters. But Sen. John McCain, R-Ariz., said that's not enough. He called for supplying the Free Syrian Army with "the support that they need to change the momentum on the battlefield" and oust Assad. That includes anti-tank and anti-air weapons that the U.S. has yet to provide.

"AK-47s don't do very well against tanks," said McCain, who has advocated for assisting opposition forces since the civil war broke out two years ago. "Give them the support that they are needed to succeed."

But concerns remain that rebels, too, are divided and that an end to the Assad regime would could open the door for al Qaeda forces to gain a stronghold in Syria.

Sen. Bob Corker, R-Tenn., said that U.S. intelligence officials "know more than we let on publicly which groups to support" but admitted there's no guarantee U.S. weapons won't end up in the hands of terror groups.

"There’s going to be mistakes," said Corker, ranking member of the Senate Foreign Relations Committee. "Some people are going to get arms that shouldn't be getting arms. But we should still be doing everything we can to support the Syrian opposition."