(CNN) Ten days before the government would run out of funding, bipartisan negotiators are still struggling to reach a budget deal, and many lawmakers on Capitol Hill are already admitting Congress will need another stopgap bill to avoid a shutdown.

The number two Senate GOP leader, John Cornyn, told CNN on Tuesday that while he "hopes" the government can avoid a shutdown, it's "likely" that there will be another short term continuing resolution to give the talks more time beyond January 19.

The Texan stressed that "the clock is ticking and we need border security and a solution for these" recipients of the Deferred Action for Childhood Arrivals program , which expires in March.

While top leaders and their senior staff are working toward a possible deal on overall spending levels for the Pentagon and domestic programs, the issue of how to address those children of undocumented immigrants who could face deportation in March is the primary sticking point holding up a funding package.

House Speaker Paul Ryan told members at a closed-door meeting that bipartisan talks are moving in the right direction, and he was pressing for separate action on DACA.

After the meeting, the Wisconsin Republican dodged a question on whether he could round up the votes for another short term bill if they needed one, telling reporters, "I am not going to get into hypotheticals. I think we're having good fruitful conversations with our members."

Many House conservatives and members of the Armed Services Committee focused on securing a major increase for the military are critical of another punt, arguing a real budget is overdue and the Pentagon is already suffering under a series of short term bills.

If House Democrats withhold support for any "continuing resolution" because of an impasse over DACA, Republican leaders could have issues getting their conference on the same page again to avoid a shutdown at the end of next week.

GOP Rep. Roger Williams of Texas said he expected some type of stopgap bill, but he wasn't enthusiastic about having to vote for another one after backing the version that passed right before the Christmas holiday.

"We've got to get back to running business with a budget and it's not something that I support," Williams told reporters Tuesday.

Republican Rep. Chris Collins of New York was blunt in acknowledging negotiators can't meet the January 19 deadline but stressed, "I would say we're going to keep the government open."

House Republicans are exactly where they were in December: divided on how to fund the government, how to craft an immigration bill that protects DACA recipients and bolsters border security, how to reauthorize a key spy program and stabilize the Obamacare insurance marketplace. Just a day after returning from recess, House Republicans are already fuming that leadership has no plan and another deadline is looming.

"They didn't talk about specifics," GOP Rep. Mark Amodei of Nevada told CNN when asked about DACA negotiations. "Shock."

Cornyn told reporters Monday night that at this point Democrats are holding spending negotiations "hostage" until they see progress on DACA.

House Minority Leader Nancy Pelosi has repeatedly insisted that discussions about a funding deal be accompanied by a plan to vote to ensure that the DACA recipients, also referred to as "Dreamers," are allowed to stay in the US.

Conservative House Republicans, who are concerned about what could come out of continued talks with the Senate, want their leadership to schedule a vote on a House GOP measure rather than wait for a bipartisan proposal that earns 60 votes across the Capitol.

"What we don't want to do is ... get jammed by some Dreamer Act bill in the Senate, which some of us are concerned about," said Rep. Mark Walker, a Republican from North Carolina. "The leadership (is) keeping their cards close to their vest right now."

But moderates who are facing re-election in districts with significant immigrant populations are growing increasingly frustrated by the slow rate of progress and are open to finding a compromise.

Rep. Mike Coffman, a Republican from Colorado who represents a large Hispanic community, said his constituents are demanding solutions not only on DACA, but also on Temporary Protected Status, a program that allows immigrants from certain countries to stay in the US. He said he was hoping to hear what the "parameters" and "schedule" for a deal would be, but he heard nothing at the closed-door House GOP meeting Tuesday.

"They barely touched on it," Coffman said. "I was hoping to hear something about DACA and TPS."

Amodei said that at this point, someone needs to make a decision about how to move forward on DACA because it's only a matter of weeks until the March 5 deadline when the federal program ends.

"As long as we are talking about concepts and not 'here's the bill,' you're just going to continue chasing your tail. You are going to continue producing nothing," Amodei said.

Those on the right of the conference continue to stress that they need more resources dedicated to beefing up border security. But while President Donald Trump focuses on a "wall" as a key component of any deal on DACA, even conservative lawmakers are signaling they can get behind a plan that guarantees more resources for other types of security.

"The wall is generically speaking -- technology, boots on the ground, [that's the way] I think of the border," Williams said Tuesday.