House conservatives are demanding changes to the GOP leadership's latest proposal to end the government shutdown and raise the debt ceiling.

Republicans initially said a vote on the new plan would take place Tuesday, but they have already hedged on those plans given demands from their members.

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“We gave a bunch of different options that I know our leaders are considering right now,” Rep. Mick Mulvaney (R-S.C.) said. “It’s just tweaks.”

“I think we are putting some good steps toward something the House would be able to support before the end of the day,” Mulvaney added.

The latest House GOP plan would modify a deal being developed in the Senate to end the shutdown, fund the government through Jan. 15 and raise the debt ceiling until Feb. 7.

The House plan would also delay for two years a tax on medical devices and scrap healthcare subsidies for lawmakers, the president, the vice president and Cabinet members who must enroll in ObamaCare, among other changes.

Under ObamaCare now, lawmakers and staff members are required to enroll through the program but can still receive the tax subsidies they get under federal healthcare plans.

Conservatives in the House want congressional staff to also be prohibited from receiving an employer contribution to help offset the costs of insurance.

Under the healthcare law, lawmakers and staff are required to enroll in insurance through ObamaCare's exchanges, but currently are still slated to receive the contribution from the federal government they now enjoy.

“We have always thought that made sense,” said Rep. Jim Jordan (R-Ohio), who said he would see if he could vote for the new plan based on talks between members and their leaders.

Rep. Charles Boustany Charles William BoustanyPartial disengagement based on democratic characteristics: A new era of US-China economic relations Lobbying world March tariff increase would cost 934K jobs, advocacy group says MORE Jr. (R-La.) said that party leadership and the conservatives were “not that far apart.”

He said the main tweak is putting original ObamaCare congressional subsidy language authored by Sen. David Vitter David Bruce VitterLysol, Charmin keep new consumer brand group lobbyist busy during pandemic Bottom line Bottom line MORE (R-La.) into the House GOP offer.

“My sense is that if the original Vitter language were in there, then we would get more support for it,” Boustany said.

If GOP leaders bring a bill to the floor, it would almost certainly have to be approved with almost only Republican votes.

The White House rejected the GOP proposal, and Democrats have panned it. President Obama is also meeting with House Democratic leaders Tuesday afternoon, a sign he is trying to get his side on the same page in the final hours before the Oct. 17 deadline set by the Treasury Department for raising the debt ceiling.

Senate Majority Leader Harry Reid Harry Mason ReidSenate Republicans signal openness to working with Biden Mellman: The likely voter sham Bottom line MORE (D-Nev.) has also warned that the House plan is dead on arrival in the Senate.

House leaders made it clear that they are listening to their members.

"We're still working through our issues," said House Budget Committee Chairman Paul Ryan Paul Davis RyanAt indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates Peterson faces fight of his career in deep-red Minnesota district MORE (R-Wis.).

Other conservatives said they were pushing language that would allow employers to opt out of providing insurance that covers birth control and other services they find morally objectionable.

Rep. Tim Huelskamp (R-Kan.), a consistent thorn in leadership’s side, said that he was worried that there were “no religious liberty protections” in the original plan.

Jordan also said the lack of a "conscience clause" was one of the planks conservatives were fighting for.

Like Boustany, conservative Rep. David Schweikert David SchweikertHouse Democratic campaign leader predicts bigger majority Democrat Hiral Tipirneni wins Ariz. primary to challenge Rep. David Schweikert Ethics watchdog finds 'substantial' evidence of improper spending by Rep. Sanford Bishop MORE (R-Ariz.) said conservatives were close to supporting their leadership's deal.

“There are a handful of things I think will make it better,” he said.

Schweikert said that Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE had handled the whole situation “stunningly well."

“Remember who I am. I’m one of the four guys thrown off his committee for being cranky,” Schweikert said. “I’m very proud of the conference.”

Boustany shot down the idea espoused by some conservative members who wanted to see more action on spending in a debt-limit package, saying such a shift simply isn't practical at this point.

"Realistically, to get a pro-growth deficit reduction in place is going to take more time, and we don't have time," he said. "We have to do something now and hopefully get into earnest discussions."

The conservative demands also allowed some GOP lawmakers to say that they weren’t sure where the proposal was headed, and what their final take would be.

“I think that we’ve got to see if the current form is the final form before I make that decision,” Rep. Jack Kingston (R-Ga.) told reporters. “I don’t think that this is the final form, and that’s just one guy’s opinion.”

But some conservatives predicted that the GOP conference would stand together, just as it has in a string of recent floor votes.

— This story was posted at 11:37 a.m. and updated at 1:04 p.m.