Washington (CNN) Democrats are increasingly grappling with the likelihood that Congress could push a decision on a popular immigration program into January, even as they've spent weeks saying it should be dealt with by the end of the year.

"To some extent, yes," Congressional Hispanic Caucus member and Arizona Democrat Rep. Raúl Grijalva said Thursday on Capitol Hill when asked if there's a growing realization that the issue will likely slip to January.

"Some of us are holdouts, but if you talk about reality, yeah," he continued. "I mean, if leadership is not pushing it, they're not holding the line with members and we have a CR that includes (children's health funding), which is really, really important, funding for community health centers, then not seeing it before the end of the year becomes more and more precarious."

Democrats and even some Republicans have not given up on trying to get done a deal to maintain a version of the Deferred Action for Childhood Arrivals program, which protected young undocumented immigrants brought to the US as children from deportation but which President Donald Trump has opted to terminate.

Advocates note the issue is more urgent than portrayed by the administration. More than 20,000 DACA recipients either did not renew or were rejected in the window the government offered, meaning more than 100 lose their status every day before the March 6 deadline the administration intended to set.

But even as negotiations continue and intensify on both sides of the Capitol to reach a bipartisan compromise on the issue, the likelihood of being able to pass something by the end of the year is rapidly slipping away.

Illinois Sen. Dick Durbin, the No. 2 Democrat, hosted a meeting of the Senate negotiators on Thursday afternoon, including Republicans Lindsey Graham, James Lankford, Cory Gardner, Jeff Flake and staff from Sen. Thom Tillis. But all exiting the meeting said while negotiations progressed, no break-throughs have been reached yet. And while some wouldn't rule it out as a possibility, none expressed much optimism it could be done by the end of the year.

"It's starting to take form, but we're still negotiating," Durbin said.

Tillis, R-North Carolina, said earlier Thursday that negotiators are working on a consensus on how to handle the DACA component of the deal, reconciling different bill approaches that are out there.

"What we're trying to do is figure out where we have common ground there," Tillis said. "But we'll be reaching a point pretty soon to where we have to have a discussion about chain migration, which is very important, the President's told us, and border security and other things. I would say when we talk about 'we're close to an agreement,' we're only talking about one half of the broader agreement, so maybe we're a third of the way there."

"I think people are having good faith discussions," he continued. "I can't imagine it being done by year end."

Strategic maneuvering

Democrats know that their greatest leverage for many of their priorities is on government funding, which expires a week from Friday. Republicans will likely need Democratic votes to pass a full year of funding, in the Senate and likely in the House where budget hawks traditionally reject domestic spending levels.

But they also have a laundry list of priorities for negotiation, including an overall deal on domestic spending, community health centers, children's health insurance, pensions and immigration. And five legislative days before funding runs out.

The current plan, according to multiple lawmakers and aides, is for the House to pass a bill that would fund defense for a year, reauthorize children's health insurance, and punt the rest into January. That bill is dead on arrival in the Senate, where 44 Democrats have gone on record opposing it. The belief is that the Senate will send something back to the House, likely with Obamacare payments or possibly just a short-term funding extension into January. All the while, parties negotiating a DACA deal in both chambers remain optimistic about the progress of talks.

Such a plan could squeeze Democrats, especially in the Senate, to weigh rejecting an opportunity to keep negotiating and risk the government shutting down, or to hold out for more offers from Republicans.

It's possible that a short-term extension could pass the House without Democratic votes, taking pressure of House Minority Leader Nancy Pelosi, who with her caucus has been more vocal about rejecting anything that doesn't include DACA by the end of the year. House Freedom Caucus Chairman Mark Meadows said many of his members, who are the more troublesome Republicans for the party on funding, could support a punt.

"If it's just looking at a (continuing resolution) that gets us to January 19 where we can negotiate on a bigger omnibus, I think most of my members will support that," Meadows, R-North Carolina, told reporters Thursday. "There are some who won't, but most would be supportive of that."

In the Senate, Democratic aides believe that January could be an option. They feel there would be no need to force a bad deal now, if a good deal is still attainable in a few weeks' time. Senators have also been more cautious than their House colleagues.

"I'm hopeful that it will happen. And we're not there yet on what will happen if it doesn't happen," Hawaii Sen. Mazie Hirono said at a press conference Thursday about pushing for all of Democrats' priorities by the end of the year, asked whether members would reject a deal to keep making progress on some issues.

Warnings to Democratic leadership

Still, Democrats are warning their leadership that they can't appear to surrender.

"I think there is a Plan A, a Plan B, a Plan C, a Plan D and a Plan E in the House, I can see that there are more heightened negotiations in the Senate, and I'm dedicated to working 24/7 and I have to say my caucus has been doing that," Congressional Hispanic Caucus Chairwoman Michelle Lujan Grisham said Thursday. "We want something to vote on next week, and we are making that clear to leadership. ... So I think we have to stay the course and any conversation that we can wait even 15 days is cruel, unjust, wrong and there's real harm."

"I'm not ready to wave the white flag and say let's see what happens," Grijalva echoed. "I think the pressure has to be constant on this thing or it will fail."

The deputy chair of the Democratic Party, Minneosta Rep. Keith Ellison, said Democratic leadership should know that the party base will not accept less than a full fight.

"My advice to anybody in leadership in the House of Representatives is we better do everything imaginable to deliver on DACA or we better we be visibly shown to have done every single thing that could be done," Ellison said. "Our grassroots base is expecting us to deliver on DACA, and that's it. ... I feel so strongly about this. We cannot fail on this."