The House Republican Study Committee chairman, Rep. Mike Pence (Ind.), predicted that as many as 18 conservative Republicans, and possibly more, would join him in killing the House budget resolution this week if House GOP leaders continued to block an RSC-led effort against spending bills that threaten to exceed budget caps.

On Tuesday, Pence walked out of negotiations with House Majority Whip Roy Blunt (R-Mo.) after rejecting what one House GOP leadership aide described as a “significant step forward for leadership” in the weeks-long talks over allowing Members to file budget points of order.

“We have held out for point-of-order protection,” Pence said.

The Indiana lawmaker also indicated that he was open to more talks.

“Ever buy a car?” he asked a reporter. “Ever walk out of the manager’s office? It helps the price.”

If no agreement is reached this week and Pence actually does have 18 or more votes against the budget resolution, the measure could fail on the House floor as long as most Democrats oppose it.

But House leaders believe that Pence, who attended the afternoon meeting with Reps. Mark Kirk (R-Ill.) and Jeb Hensarling (R-Texas), may be overstating his support among RSC members. They warned him not to push too far.

“He appears to no longer be negotiating for the Republican Study Committee,” said the House GOP leadership aide. “He can either be a part of the solution or walk away and take nothing.”

The aide also noted that the House would stay in session through the weekend if necessary to force votes on the budget resolution.

“We’ll stay here as long as it takes to pass a budget, and at the end of the day, we’re confident we will,” the aide said.

Pence, however, vowed to stand his ground and said GOP leaders were wrong in suggesting that he did not have the votes to prevent the budget from passing.

“The only vote that Mike Pence controls is Mike Pence’s vote,” he said. “But it is my judgment that many of my colleagues are very much in agreement with me that we have to change the way we spend the people’s money.”

One House GOP aide noted that many RSC members reiterated their support for Pence’s stance at a meeting Tuesday afternoon.

The leadership offer included allowing rank-and-file members to call for a meeting of the full House Republican Conference to discuss budget-busting bills. Currently, 50 members must sign a petition to call for a full Conference meeting, but the proposal would have slashed the number of required signatures to 25.

“That’s a conversation, not enforcement,” complained one aide to an RSC member. Plus, that proposal is not even supported by all GOP leaders, the aide noted.

Leaders also offered to not bring up bills that break budget caps under and expedited floor procedure known as suspension of the rules. Another proposal would have required the House Rules Committee to explain to Members the reasons for waiving budget points of order on the floor.

But Pence complained that, under the proposed compromise, leadership could still waive points of order against all bills — the very practice he said he is trying to end. Currently, the Rules Committee commonly writes rules for floor consideration that prevent Members from bringing budget points of order against most measures.

Pence said he and his supporters pared back their original demand for a two-thirds majority to waive budget points of order on all bills, changing it into a proposal that allows budget points of order on spending bills only. Under Pence’s revised proposal, those could be waived by a simple majority.

But the House GOP leadership aide said the leadership has opposed Pence’s demands because allowing points of order on spending bills would “be giving the minority a tool to obstruct and sabotage conference reports. … It can be used for things other than what he’s intending it for.”

Meanwhile, House Budget Chairman Jim Nussle (R-Iowa) declared at a news conference that — assuming he can secure passage of his budget this week — the House and Senate are unlikely to be able to reconcile their different budget blueprints.

“I think the challenge for us is the Senate. It’s very disappointing to watch what’s going on over there,” said Nussle. “I am not sure how we get a conference with the Senate with the product they have.”

He added that he might have to use procedures to “deem” budget caps in the House — a move the House was forced to take last year after the House and Senate failed to reach a budget agreement.

Nussle’s comments came as it became increasingly likely that a handful of Senate Republicans would vote to eliminate the budget resolution’s call for $14 billion in cuts to Medicaid.

Sen. Gordon Smith (R-Ore.) said he had more than 51 votes for his Medicaid proposal. However, Smith said his amendment “should not doom the budget,” and he said he would likely vote for any conference agreement that did not include his amendment.

The White House and Senate Republican leaders were working to head off what could be a major embarrassment for the party if Smith’s amendment is adopted. Sen. Trent Lott (R-Miss.) said he was working on a possible compromise, but he declined to offer specifics. Still, Lott said his plan would “probably not” work.

Meanwhile, Senate Budget Chairman Judd Gregg (R-N.H.) dismissed Nussle’s comments as premature given the fact that the Senate has just begun debate on the measure.

“Maybe he just got up on the wrong side of the bed this morning,” said Gregg. “I think our budget will be very much a conference-able item.”

Ben Pershing contributed to this report.