The clock is ticking down for the supercommittee to reach a breakthrough deal on the deficit, with House Republicans’ 48-hour rule for considering bills before they come to the House floor pushing the Wednesday deadline up to Monday.

On ABC’s “Top Line” today, one of the top Republicans in the House said the urgency around the timing is real. He suggested that the timeline could be adjusted to accommodate a late deal – though he hastened to add there’s little appetite for that in House leadership.

“It’s hard to overstate the urgency in terms of the timing on this,” said Rep. Peter Roskam, R-Ill., Republicans’ chief deputy whip. “My hunch is that all 12 of those members are feeling the pressure and because, if a supercommittee deal doesn’t come together, then obviously sequestration kicks in and that’s not a remedy that is anybody’s first choice.”

In terms of the timing, “you’ve got procedures that are in place, and then you’ve also got to get things to the Congressional Budget Office in terms of scoring,” Roskam said. “Now the reality is that when it all comes down to it, the House can work its will, and it could suspend a rule if it wanted to. I don’t think anybody has an appetite to do that. So I think you’re looking at a real early deadline of early next week.”

Roskam said he’s not going to pre-judge the supercommittee’s work product: “Everybody will have an opportunity to weigh in on this thing, and on balance, that’s a good thing. The process matters.”

He also urged his Democratic colleagues to vote for a Balanced Budget Amendment; most didn’t, and the measure fell short of the two-thirds majority it needed to pass today.

“The time has come, and I think it would be an incredibly buoyant thing to do all the way around,” Roskam said. “Let’s let the country decide. Let’s let every state legislature take that up.”