The Republican leadership is walking a fine line between negotiations with Democrats and appeasing its own conservative members, who are unwilling to raise the debt limit if their demands are not met -- which include a repeal of the health care law passed last year.
"There's not a lot of time, and it's difficult from the outside to see how our leaders could reach an agreement about a fundamental change in Medicare, a fundamental change in Social Security, really big ticket changes," Marron said.
"A lot of the discussion, at least until very recently, has been about paring the debt limit increase with things that you might view as being more budget process kinds of tools -- discretionary spending caps, triggers -- where Congress would try to set out a vision of where it wants the fiscal posture to go, but then doesn't yet make the specific decisions about how to accomplish it," he added.
While such a move may avert a debt crisis, it's unlikely to appease Tea Party members and those members of Congress who came to the House on the back of their support. Many of them say they want to see not only big spending cuts, they want to see them now.
At a Tea Party gathering Monday, attendees blasted both Boehner and Ryan for not being aggressive enough and threatened to take them out of office if they continued down that path. The event was endorsed by Minnesota congresswoman and presidential hopeful Michele Bachmann.
The Republican Study Committee, a group made up of some of the most conservative House members, is planning to unveil its own conditions for raising the debt ceiling later this week or next week.
The committee is keeping details under lock and key, but a report by Politico suggested that the proposal will call for immediate spending cuts, spending caps at 18 percent of GDP and a balanced-budget amendment.
"[The] proposal is absolutely going to be focused on making sure that we are cutting spending and making reforms that keep it down and ensure that we're not just promising future cuts, but that we're actually doing them today, and making sure that what's promised for tomorrow actually occurs," a Republican aide told ABC News of the RSC proposal.
ABC News' John Parkinson contributed to this report.