Story highlights The crux of the issue is finding a way to get moderates and conservatives on the same page

The sagging mood among Senate Republicans marks a new low point for McConnell

Washington (CNN) Republican senators returning to Washington Monday sounded exasperated and downright deflated about their unpopular bill to overhaul the health care system.

Some are even beginning to wonder out loud what was an unthinkable prospect a year ago: the GOP could be forced to ditch its efforts to get rid of Obamacare.

"Better than 1%. Not yet above 2% in my opinion," a senior Republican source told CNN on the chances the health care bill will pass Senate at this point.

Fresh off the recess, members seemed to be unclear on how Majority Leader Mitch McConnell could bridge the divide within the conference.

"I think we have the information we would need if we're willing to use it. If we're willing to be honest about what has caused the collapse of these markets and address it forthrightly, not being concerned about the political implications, but actually fix the problem," said Sen. Ron Johnson, a Republican from Wisconsin who has been vocal about his frustration with the process. "I think we have the information to address it. I'm not sure we are going to address it, and that is enormously frustrating for me."

Read More