(CBS News) WASHINGTON -- The White House spent the Labor Day holiday hard at work, using every means possible to try to win over skittish lawmakers on military strikes against Syria.
Many members of Congress still have grave doubts, even after Monday's conference calls, briefings and in-person meetings, but two key lawmakers offered their support.
Emerging from a meeting with President Barack Obama Monday, Republican Sens. Lindsey Graham and John McCain said the president assured them he had a strategy to strengthen the rebels and weaken Syrian President Bashar Assad's regime.
"There seems to be emerging from this administration a pretty solid plan," Graham said.
Both senators agreed to sell the plan to skeptical colleagues in advance of a vote next week.
"A rejection of that, a vote against that resolution by Congress, I think, would be catastrophic because it would undermine the credibility of the United States of America and the president of the United States," McCain said. "None of us want that."
About a hundred members raced back to Washington for a classified briefing on Capitol Hill after President Obama took Congress by surprise Saturday when he announced he would seek its authorization before launching missiles.
They emerged dubious about the rationale for strikes.
"The mood from my district is to not do this," said Texas Republican Michael Burgess.
"I think a lot of us are concerned," California Democrat Janice Hahn said. "Where is the international community? If this is such an outrage, if this is so abhorrent to everyone, where's the outrage?"
With his reputation riding on this vote, the president reached out to some skeptics by phone and will meet with the leaders of six key congressional committees at the White House Tuesday morning.
Secretary of State John Kerry, whoover the weekend, is being dispatched to Capitol Hill for a series of hearings this week, along with Secretary of Defense Chuck Hagel and Director of National Intelligence James Clapper.
They will be challenged by members who feel that the formal resolution drafted by the White House essentially gives the president a blank check to use whatever kind of force he wants. White House officials said today they are open to changing the language, making it more narrow, before Congress votes on the resolution sometime next week.
It's an issue that doesn't divide neatly along party lines. Some of the president's biggest supporters oppose striking Syria, while some of his biggest detractors support it. Some are still trying to decide how they feel about a complicated international issue, as most members did not think they would have any input on the president's decision strike Syria until his announcement this weekend.