President Donald Trump talks with House Speaker Paul Ryan (R-WI) as he promotes a newly unveiled Republican tax plan with House Republican leaders in the Cabinet Room of the White House in Washington, November 2, 2017.

Congress is barreling toward a Dec. 8 deadline to avoid a government shutdown, but there's one tug-of-war they don't expect to start until the new year: Raising the debt ceiling.

A House Republican working group gathered Tuesday evening to discuss a list of debt ceiling priorities to consider when the urgency of keeping government open is a non-issue, according to multiple meeting attendees and a copy of the list obtained by CNBC.

The proposals mostly concern traditional Republican efforts to enforce the budget and instill spending discipline: By requiring a signature from the president; subjecting all spending, even mandatory spending, to the appropriations process; instituting "difficult to bypass" spending guardrails; making the process for short-term deals more onerous; or reforming Social Security and Medicare.

One particular proposal — tying spending caps and the debt ceiling to economic growth — led to a heated discussion in which attendees questioned whether such pegs would be arbitrary or even feasible.

"Most people admitted that going from 'big idea' to 'legislative text' would be immensely challenging," said one attendee who spoke on the condition of anonymity because the group's deliberations are private. "Strangely, there was no word at all about the looming debt ceiling deadline," this attendee said, noting the group's conversations categorized the ideas as "for next year."

A senior White House official told CNBC that deliberations will likely come to a head in January after one or two continuing resolutions, since Congress remains in the thick of tax reform. Treasury will know by Dec. 15 how much longer it can creatively finance debt payments based on the tax receipts it tabulates, this official said. Congressional aides said members have been told the debt limit could be reached in February or March.

Rep. Doug Collins, R-Ga., whom House Speaker Paul Ryan tapped to lead the debt ceiling group, said in an interview that the group would prefer to make lasting changes than small tweaks in this cycle.

"I would not tie current events to a working group that is looking for long-term solutions," Collins told CNBC. "The benefit, up or down, of this group is not what happens in the next three weeks."

Even so, members of the group that spoke to CNBC anonymously had hoped to provide a list of concrete proposals to Ryan by Dec. 1, or a week before the Dec. 8 funding deadline and described the Tuesday meeting as a "Come to Jesus" moment and "crunch time."

Collins said he speaks regularly with Ryan about the group's discussions, including Wednesday following the meeting. An email circulated Wednesday evening to the group said a meeting with members and Ryan is in the works to chart "a path forward."

Ryan assembled the working group in early October after President Donald Trump sided with Democratic leaders to suspend the debt limit for three months. More than half of the group's members voted against the September deal. The group represents widely varying ideologies within the party — from fiscal hawks demanding caps on spending to moderates who wouldn't mind a "clean" debt limit increase if it spares the full faith and credit of the United States.

Bipartisan support would be needed to raise the debt ceiling, and Democrats had sought to secure passage of legislation to protect "Dreamers" in exchange. In September, Senate Majority Leader Mitch McConnell said the Treasury's ability to prioritize certain payments, an exercise termed "extraordinary measures," meant Republicans could decouple the two issues by dealing with government spending first and the debt ceiling later.

"I can confidently predict there will not be a connection with the debt ceiling and spending decisions in December," McConnell said in September. "It doesn't mean we won't have to address the debt ceiling at some point, but it will not be in December."

Immediately following Trump's debt deal with "Chuck and Nancy," discussions followed on how to "de-politicize" the debt ceiling so it doesn't require horse trading so often. The White House then pivoted to tax reform, and it's unclear how President Trump's views have evolved since then.

This week, the president tweeted "I don't see a deal!" with Democrats on government funding, leading Senate Minority Leader Chuck Schumer and Nancy Pelosi, the top-ranking Democrat in the House, to skip a White House meeting on that topic.

A senior administration official told CNBC that the president would in theory support a move to re-link the debt ceiling with the annual budgeting process — a move that would automatically raise the debt ceiling when Congress approved a budget resolution and scrap the need for a separate vote.

Collins said, based on what he knows about his members' positions, the White House would be met with resistance.

"Fiscal conservatives like myself would say, 'We're just hiding an issue here,'" Collins told CNBC. "We need to make some long-term restraints."

—By CNBC's Kayla Tausche. Follow her on Twitter: