Three members of Syrian President Bashir Assad's government have resigned to protest the killings, it was reported on CBS' "Face the Nation."
Sen. Mark Kirk, R-Ill., called on the U.S. government to use diplomatic pressure to undermine the Syrian regime but stopped short of supporting any kind of military action.
"I think the U.S. military is now overstretched with four major missions in Iraq, Afghanistan, Libya, and Japan," Kirk said.
Calling Syria a "far greater threat to Israel and the Middle East," Sen. Richard Blumenthal, D-Conn., said the government should encourage a democratic uprising there but take care not to begin an open-ended military operation.
Schieffer asked the senators, along with Sen. Chris Coons, D-Del., Rep. Tim Griffin, R-Ark., and Rep. Joe Walsh, R-Ill., about a CBS poll last week that concluded 75 percent of Americans disapprove of the job Congress has been doing.
"You really hear how people are still hurting, struggling to stay in their homes, to find jobs, to make ends meet," Blumenthal said, citing fuel prices topping the $4 mark.
"As someone who worked in the private sector for a long time and then ran a local government before coming here, at times I'm so frustrated, I feel like I'm banging my head against the wall trying to encourage forward movement," Coons said of working in Congress.