(CNN) Sens. Susan Collins and Lamar Alexander announced Wednesday that they will not push for a controversial health care payment to be included in a short-term spending bill, citing concerns that it could lead to a year-end government funding showdown between the House and Senate.

The move comes just after Senate Republicans passed their much-anticipated tax bill on the Senate floor early Wednesday morning. Collins, who secured several other provisions in that tax bill including a state and local tax deduction, had also gotten assurances from Senate Majority Leader Mitch McConnell that she would get a vote on two Obamacare market stabilization bills by the end of the year. The first bill would temporarily restore cost-sharing reduction payments , which help cover the health care costs of low-income Americans in exchange for market reforms. The other legislation would help shield insurers from high-cost patients in the wake of Republicans repealing the individual mandate in their tax bill. The individual mandate, which requires that Americans have health insurance or face a fine , is important because it draws younger and healthier consumers into Obamacare.

Without it, health care experts have warned insurers will likely hike premiums since more of their customers will be older and sicker.

But despite voting for the tax bill, Congress will leave before taking up Obamacare funding.

"Rather than considering a broad year-end funding agreement as we expected, it has become clear that Congress will only be able to pass another short-term extension to prevent a government shutdown and to continue a few essential programs," the senators said in a statement.

Collins had real assurances from McConnell that aides say were not given lightly that the health care bills would be delivered by the end of the year, but the politics of the House of Representatives complicated the matter.

McConnell doesn't control the House. In fact, the majority leader doesn't hold much cache there at all. Members -- and not just the usual conservative suspects -- revealed earlier this week they're exasperated by the number of time they feel like they are forced to back whatever the Senate sends them . And, just because McConnell promised Collins a bill doesn't mean they'll deliver: especially on something that many view as propping up Obamacare, a law they despise.

"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."

In her statement, Collins said that House Speaker Paul Ryan called Wednesday "and said that the House remains committed to passing legislation to provide for high-risk pools and other reinsurance mechanisms similar to the bipartisan legislation I have introduced."

"He pointed out that by waiting until early next year, we will be able to use a new (Congressional Budget Office) baseline that will result in more funding being available for reinsurance programs that have been proven effective in lowering premiums while protecting people with pre-existing conditions like diabetes, heart disease, and arthritis," Collins said.

Most health care experts say funding the cost sharing reduction subsidies at this point would do little to help lower rates. Insurers have already priced the absence of the subsidies into their 2018 plans.

The additional funds to cover high-cost consumers -- called a reinsurance fund -- would be more effective at reducing prices for 2019.