On Tuesday, Obama scheduled a meeting with leaders of the House and Senate armed services committees, the foreign relations committees and the intelligence committees.
On Tuesday afternoon, Secretary of State John Kerry, Defense Secretary Chuck Hagel and Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, are scheduled to testify publicly before the Senate Foreign Relations Committee. Earlier Tuesday, other members of the administration's national security and intelligence teams were to hold a classified, closed-door briefing for all members of Congress. A similar session was held Sunday and more will be held Thursday and Friday.
Kerry will also testify Wednesday before the House Foreign Affairs Committee. Kerry and Director of National Intelligence James Clapper will hold a classified briefing Wednesday with members of the Senate Foreign Relations Committee.
Members of the House Democratic caucus participated in an unclassified conference call Monday with Obama national security adviser Susan Rice, Kerry, Hagel, Clapper and Dempsey.
Following their White House meeting, McCain and Graham, who often speak in unison on foreign policy matters, said they were more inclined to back Obama's call for military action against Syria if it helps destroy the regime's missile launching capabilities and if the U.S. commits to provide more assistance to Syrian opposition forces.
"A degrading strike limited in scope could have a beneficial effect to the battlefield momentum," Graham said. "There will never be a political settlement in Syria as long as Assad is winning."
McCain, who was the Republican presidential nominee in 2008 and lost to Obama, said Obama clearly was asking for his help in rounding up votes. "I don't think he called us over because we're old campaign pals," he joked.
A senior state department official said Kerry called Syrian rebel commander Salim Idris on Monday to discuss Obama's decision to seek congressional authority and to express confidence that U.S. military action would hold Assad accountable for the use of chemical weapons, deter his behavior and degrade the regime's ability to carry out such attacks. He also stressed the need for a "strong and unified moderate opposition."
As recently as Saturday, McCain and Graham issued a joint statement saying they could not support isolated military strikes that were not part of a broader strategy to change the momentum of the civil war and result in Assad's removal from power.
After Monday's meeting, McCain said: "Now we are talking about ways of approaching this issue in a way that could be effective. We've got to see more, but at least they are talking about some options that I think could work. "
Asked whether Obama would expand his targets in Syria, McCain alluded to the Navy's decision to place two aircraft carriers in the Arabian Sea. The USS Truman arrived in the region to take the place of the USS Nimitz, which was supposed to head home. But the Navy ordered the Nimitz to stay for now.
"I don't think it's an accident that the aircraft carriers are in the region." McCain said.
U.S. officials, however, have described the decision as prudent planning and have said it doesn't suggest the Nimitz would play a role in any possible strikes in Syria.
Associated Press writers Bradley Klapper, Donna Cassata and Matthew Lee contributed to this report.