(CNN) Congressional Republicans are cheering a major win as tax reform makes its way through Congress to President Donald Trump's desk but they could be barreling toward a government shutdown at the end of the week because of a major fight between House and Senate GOP lawmakers over Obamacare payments.

Unless they pass a stopgap funding bill before a midnight Friday deadline, federal agencies' coffers run dry.

"It's kind of like leaving the hospital just finding out that you are cancer free and getting run over by a Mack truck," Rep. Mark Walker, a North Carolina Republican who's the head of a group of fiscal conservatives, told reporters Tuesday, ticking off his concerns about following the tax vote with an expected push by Senate GOP leaders to add Obamacare subsidy payments to a must-pass year-end bill, plus support a massive disaster aid package without any offsets to other programs.

House GOP leaders informed rank-and-file members that they planned to attach an $81 billion disaster aid bill to their version of the spending measure, which includes a full-year defense funding bill. They are aiming for a House vote Wednesday, but they will need to pass that version without help from Democrats, who complain they've been left out of negotiations.

But the Senate isn't expected to accept that legislation, as Democrats have insisted that any spending agreement include a deal for domestic programs in addition to the Pentagon. Instead, senators are expected to strip out the defense portion and send a bill back to the House that includes funding for cost-sharing reduction payments -- a move that has House GOP members from across the ideological spectrum seething.

They are crying foul that Senate Majority Leader Mitch McConnell made a deal to add so-called "CSR payments" to the funding bill in order to secure Maine Sen. Susan Collins' vote for the tax package. These subsidies for health insurers help cover the cost of insuring low-income individuals in the Obamacare marketplace.

"We did not give her that assurance," GOP Rep. Bradley Byrne of Alabama told reporters Tuesday, saying that many forcefully informed House Speaker Paul Ryan that move was unacceptable. "She may have gotten that assurance from the leadership of the Senate. She did not get assurance from anybody in the House."

It's not just those on the right -- who regularly vote no on short-term spending bills -- who are pushing back, which signals that an impasse over the issue just ahead of the deadline could keep Congress in town longer than their scheduled departure Friday for the holiday break.

"That thing put on the floor on its own would fail spectacularly, and we don't owe that kind of concession to them," said Rep. Tom Cole, a Republican from Oklahoma. "The speaker made it abundantly clear that while the Senate leadership is fee to make whatever commitments they want in their body, to their members, that does not apply to our body and our members. If we get into that kind of game, I think it will be very destructive."

"There is not the consensus within our conference to support that," said GOP Rep. Mark Meadows of North Carolina, the chairman of the conservative House Freedom Caucus.

Multiple House Republicans and aides say they won't go along with a last-minute effort to again try to force GOP members to swallow something the Senate decides to add on, and could instead continue the legislative pingpong, taking what the Senate sends back, removing the CSR provisions and shipping it back for the Senate to vote on. This would mean that again, Congress would be brushing up against the brink of the deadline to keep agencies running.

Cole emphasized that Republicans from both bodies need to stay in town until the government is funded -- despite threats from some in the House to skip town.

"If we can't come to a deal, you need to be prepared to stay," Cole said. "You can't in good conscience leave town and let the government shut down. ... If we have to do day-by-day CRs until we pass a deal, fine with me."

Even Democrats, who have called for months for a vote to ensure the subsidies continue to be paid, are signaling that they aren't prepared to help the GOP come up with the votes on the Obamacare subsidies to avoid a shutdown.

The number two House Democrat, Rep. Steny Hoyer of Maryland, said the bipartisan Senate deal to continue paying insurance companies subsidies for Obamacare was a "very constructive effort" but that it should have been approved months ago.

He said it's too late now to affect the marketplace: "We don't think it's going to very substantially affect, if at all, rates for 2018. They've been set; policies have been bought."

Rep. Jim Jordan of Ohio, a member of the conservative House Freedom Caucus, said he's been unequivocal that including a bill to pay for CSRs won't fly. The group planned a meeting for Tuesday afternoon to huddle on strategy for the next steps.

"If it's got (a deal on CSRs) on it, that's a big problem for a lot of us," Jordan said.

Top House GOP leaders are hoping that McConnell decides to punt any action on CSR payments until early in 2018, but they are still working to figure out next steps. The uncertainly comes as members are celebrating a huge win and eager to go home for the holidays to emphasize a major legislative achievement.

"Never underestimate our ability to step on a good story," Cole said. "We're great at it."