Sen. Chuck Grassley (R-Iowa) also raised the issue of the national debt, signaling what might prevent many Republicans from getting on board.

"I think there would be less chance of that now considering the great big budget deficit we have now," Grassley said. "We're in a much worse situation."

So how would he vote if a measure were brought to floor to back pay federal employees?

"I would not make a judgement at this point," Grassley responded.