By Deirdre Walsh, Lauren Fox and Manu Raju

The battle over a government shutdown appears to be over for now, with the push over paying for a border wall sidelined.

But one key sticking points remains before a deal is finalized -- on health care, again.

At issue: Money the federal government pays health insurers to reduce the out-of-pocket costs for low-income people trying to pay for health care. These are referred to cost-sharing reduction (CSR) payments. The payments are a major way Democrats ensured low-income people would be covered under the Affordable Care Act, but with a new Republican administration, their future is uncertain.

The fight over subsidies means there is a growing possibility on Capitol Hill to fall back on a week-long funding bill extension to avoid a shutdown and keep the negotiations moving forward, but few think the subsidies issue would lead to a shutdown.

A senior GOP aide familiar with the talks told CNN the standoff will ultimately need to be resolved by the President in consultation with House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell, but no one expects it to block a deal in the end.

Democratic House Leader Nancy Pelosi spoke Tuesday with White House budget director Mick Mulvaney, telling him that the payments must be included in the spending bill, according to a senior Democratic aide familiar with the conversation. Mulvaney indicated that, while the Trump administration had continued the CSR payments, they had not yet decided whether they would make the May payment, according to the source.

If the Trump administration stops making the payments, insurers could try to pull out of Obamacare immediately, leaving up to 7 million people scrambling to find new -- and costlier -- policies. Many insurers have said they would likely exit Obamacare completely for 2018 or hike rates substantially -- by 20% or more, Anthem said Wednesday morning -- if the subsidies end.

Democrats want assurances in the spending bill that Republicans will continue making the payments. A senior Democratic aide told CNN that "the position of House and Senate Democratic negotiators is that the omnibus must include the CSR language."

The GOP aide said that Pelosi and Mulvaney restated their positions ‎last night, and said the Democrats highlighting this fight is a "negotiating tactic."

"It's not insurmountable" the aide said, but admitted the talks "are going slower than expected."

Ryan rejected the Democrats' push on Wednesday morning.

"We're not doing that," Ryan told reporters, arguing that it is an issue that is not part of the annual spending bill process.

Mulvaney told CNN's Jake Tapper on Tuesday that Democrats had made their request on Obamacare subsidies too late in the negotiating process.

"They dropped this Obamacare bailout, these insurance company payments, about two weeks ago," Mulvaney said. "These are things they've brought to the table very late."

Insurers are desperate to get some clarity on the issue and make sure the administration continues making the payments.

But, Republicans argue that the payments are part of mandatory spending and therefore shouldn't be part of the negotiations.

Administration officials on Tuesday highlighted the concession of the border wall of sign of being reasonable and flexible negotiators to avoid a shutdown.

"We just thought that it would be a good first step to get these things that everybody agrees on and take that idea of a government shutdown off the table," Mulvaney told CNN.

White House Chief of Staff Reince Priebus said Tuesday evening that Trump is "showing some reasonableness on the wall and border security" in an effort to avoid a government shutdown.