Emerging from a closed-door session with President Obama, Republican Sens. John McCain (Ariz.) and Lindsey Graham (S.C.) said Congress needed to authorize the use of force to address the Syrian crisis or risk undermining the credibility of the president and the United States.

“If the Congress were to reject a resolution like this, after the president of the United States has already committed to action, the consequences would be catastrophic, in that the credibility of this country with friends and adversaries alike would be shredded,” McCain told reporters. “And there would be not only implications for this president, but for future presidencies as well.”

“Both Senator Graham and I are in agreement, now that a resolution is going to be before the Congress of the United States we want to work to make that resolution something that the majority of members of both houses can support,” he added.

“We still have significant concerns,” McCain added. “But we believe that there is in formulation a strategy to upgrade the capabilities of the Free Syrian Army and to degrade the capabilities of Bashar Assad. Before this meeting, we had not had this indication. Now the question is whether that will be put into a concrete strategy that we can sell to our colleagues, and that we can agree with.”

“John and I both would like a more sustained military effort, but we understand where the president is at on that issue,” Graham said. “But it is my hope that even a limited military strike can degrade Assad’s ability to project force, especially chemical weapons.”

While the senators emphasized several points of common ground with the president, including opposition to sending ground troops, they also criticized Obama for failing to clearly articulate what’s at stake for the American people.

“The president, really, has no one to blame, in many ways, but himself about the lack of public understanding of what’s at stake in Syria,” Graham said.

McCain expressed concern about how long it had taken Obama to deploy American force. “Now it’s been over a year since the president said it would be a game changer if chemical weapons were used,” he said. “It’s been two years since the president said [Syrian president] Bashar Assad must leave.”

Graham said he suggested to Obama that leaders of the Syrian opposition make their own case directly to Americans, and pledge that if they take power in Syria the country’s chemical weapons stockpile would be turned over to international authorities. Only by emphasizing that inaction would encourage Iran to develop its nuclear capacity, he added, would the American people accept a military strike.

“So what can I sell to the people in South Carolina? I can’t sell another Iraq or Afghanistan, because I don’t want to,” he said, adding that if it manages to “deter Iran from a nuclear weapons march, and stabilize the region… Most South Carolinians get that point.”

Still, McCain said administration officials “have a selling job to do.”

“I think they’re going to have to work very hard,” he said. “Americans are very skeptical.”

Anne Gearan contributed to this report.