Most Republicans now believe funding for U.S. wars should be offset with spending cuts elsewhere, a top GOP senator said Wednesday.

Sen. John Thune (R-S.D.), the chairman of the Republican Policy Committee, said there was no consensus within the Senate GOP, but a growing number of their members are insisting that war funding bills be deficit-neutral.

"Frankly, I think there's even a growing consensus among Republicans that we need to start budgeting for this, we need to figure how to pay for it," Thune said. "And I think that's kind of the majority view among Republicans now."

"We've got a lot of Republicans who now believe that even the war spending now should be offset and ought to be budgeted for," Thune said on ABC News's "Top Line" webcast.

Republicans have been adamant that Democrats' spending initiatives, such as extensions in unemployment insurance or other federal benefits, be offset by spending cuts elsewhere in the budget. Wartime spending has almost always been treated differently, however, because any effort that holds up its passage would defund troops in battle and open up a potential political vulnerability.

Concerns about the growing deficit had mounted to such a point that even Democrats were nervous at passing normal spending bills without some nod toward offsets, Thune said, adding that President Barack Obama had "reached the limits" of his ability to sway congressional Democrats on spending.

Thune said that, at the very least, the items in war spending bills that don't relate directly to troop action on the ground should be budgeted.

"I think right now what you're seeing is a growing concern — not just among Republicans have always been there — among Democrats in both the House and the Senate about this increasing amount of federal debt," Thune said. "There's less and less of an appetite to do things now that involve spending money that's not paid for, not offset."