After nearly three hours behind closed doors, senators left a classified hearing on Syria unswayed by testimony from Defense Secretary Chuck Hagel and Chairman of the Joint Chiefs of Staff Gen. Martin Dempsey.

Members of the Senate Armed Services Committee were briefed in secret on the "scope" of President Obama's proposed military strike on Syria in retaliation for its use of chemical weapons against its own people, Sen. Ted Cruz, R-Texas, told reporters.

Armed Services Committee Chairman Sen. Carl Levin emerged from the meeting and announced that he would support the resolution authorizing military force that is now circulating in the Senate, despite polls showing that a majority of Americans oppose such an action.

"It may be a close vote, it may be a divided vote," Levin, D-Mich., said, comparing it to the vote that authorized the invasion of Iraq – which he voted against, despite popular opinion in favor of the resolution at the time. "It's a vote that we all have to make according to our best judgment. What public opinion will be at that time, we don't know."

Sen. Jeff Sessions, R-Ala., told reporters that he and other lawmakers have been receiving “very negative phone calls” from constituents, and that although he was undecided, it was clear to him that “the American people are very dubious about deeper involvement in the Middle East.”

But in a comment reflective of what many in Congress are now thinking, Sessions added that the president had to clearly articulate where a potential Syria strike would lead the United States.

“The United States is not able to respond to every violation of every international treaty around the world whenever that happens,” he said.

Wednesday's closed briefing — along with a series of hearings and phone calls that the Obama administration has provided lawmakers – appear to have done little to convince senators to change their minds.

Sen. Jim Inhofe, R-Okla., the top-ranking Republican on the committee, said he still opposes a military strike.

"Nothing has changed my position initially to oppose it. ... They have decimated the military, this administration, [through defense cuts]," he said. "We're just not in any position to take on any major confrontation."

Inhofe's Republican colleague, Senate Intelligence Committee Co-Chairman Sen. Saxby Chambliss, R-Ga., said he found the hearing "somewhat informative" but that his position remained the same: He supports a military strike.

"I've been supportive of taking action all along," Chambliss said, "and nothing I've heard has changed my mind."

Plenty of senators remain open to the possibility of a strike, telling reporters they had not yet decided how to vote on a resolution authorizing military force.

"I'm undecided," Sen. Deb Fischer, R-Neb., said bluntly, echoing the remarks of many senators who left the briefing without speaking at length with the press. "It's a closed hearing. I'm not going to speak about it."