"We have to have a plan. It has to be a strategy. It can't just be, in my view, pinprick cruise missiles," McCain said, echoing what he and Graham said in a statement this weekend, which said while they support military intervention they "cannot in good conscience support isolated military strikes in Syria that are not part of an overall strategy that can change the momentum on the battlefield, achieve the President's stated goal of Assad's removal from power, and bring an end to this conflict, which is a growing threat to our national security interests."
This won't be the first time the president turned to the two Republicans, one who happens to be a former presidential foe, for counsel. Obama asked McCain and Graham to travel to Egypt in early August to assess the situation and to urge the Egyptian military to proceed with new elections.
Of course, there are many other lawmakers, a bipartisan group of both Republicans and Democrats, who disagree with McCain, as well as the president, and don't want to see military action at all. In talking to lawmakers Sunday, several intimated to ABC News that they believe it would fail.
"I'm not there yet," Rep. Janice Hahn, D-Calif., said after the briefing. "I am hoping to find an answer to the question, is there another way to hold Assad accountable?"
Rep. Elijah Cummings, D-Md., added, "There's a lot more questions I have to have answered. I want to know exactly what the game plan is."
The president, as well as Secretary of State John Kerry, have said while the president is seeking authorization from Congress, he has the power to act even if the vote fails.
Many members Sunday complained that the administration's resolution is too broad and gives the president too much discretion for what has been described as a "limited" and "narrow" strike.
"The biggest single concern among the members may very well have been a very broad request for authority with supposedly a very narrow intent to do anything and I think that has to be narrowed down in the next week," Sen. Roy Blunt, R-Mo., said.
"At the same time, the limited willingness to do anything that would actually change events on the ground except discourage further use of chemical weapons is something that members, including me, are going to have to deal with whether or not that limited effort is worth the next step."
Blunt said that new language is more than likely to come about before Congress takes the vote.
"The administration is open on the language issue and I think they will have to be if they want to get their language through Congress," Blunt said.
The administration's efforts continue Tuesday when Kerry and Secretary of Defense Chuck Hagel will testify at a Senate Foreign Relations Committee hearing, a Senate aide confirmed.
ABC News' John Parkinson contributed to this report.