Sen. Johnson: President has backed us into a corner

After a hearing on Syria that lasted more than three hours Tuesday, Sen. Ron Johnson says he didn't get an answer on what he perceives as the biggest threat to U.S. national security interests: chemical weapons falling into the wrong hands.

"If the result of our action really was the fall of the Assad regime, are they prepared to do what's necessary to make sure that those chemical weapons don't fall into the hands of al Qaeda- backed rebels?" Johnson asked. "I didn't get that answer."

The Wisconsin senator and member of the Senate's Foreign Relations Committee said Syria poses a threat to national security but struggled with the administration's current case for military action.

"They're making the case that obviously Assad crossed a line using chemical weapons," he said. "From my standpoint, it's the out-of-control nature of the chemical weapons and the loss of credibility of America that is really now at stake because this President has really backed us into a corner and drawn the red line."

(Read more:Syria action would send 'message' to US enemies: Menendez)

Johnson said another lingering question is how the administration intends to cripple the Assad regime in a limited strike.

"Obviously they stated this was going to be a limited strike, designed to hold Assad accountable, deter him and degrade his capabilities," he said. "But at the same time they're not willing to change the conditions on the ground. To me, this just isn't making sense yet."

Weary of the more than decade-long war in Afghanistan, Johnson said he needs firm commitment to a timeline from the Obama administration.

"If this President is going to commit our military to action, I want to make sure that he's committed to winning, and I'm just not quite sure of that yet."

(Read more: As Syria boils, Obama looks to Congress for next steps)

Johnson said he is hoping to get answers to some of these questions in a classified Senate Foreign Relations Committee hearing Wednesday. But he added President Obama most importantly needs to answer the questions of the American people.

"He hasn't even talked about Syria for the last two and a half years, and now all of the sudden we're at this crunch point," he said. "Our options are all very limited. They're very bad, worse than they were two and a half years ago. But it's up to the President to make the case to the American public, and I hope he does it effectively."

--By CNBC Associate Producer Elizabeth Schulze. Follow her on Twitter @ESchulze9