Kevin Wurm/Reuters
The US Capitol.
CNN  — 

Congress appears no closer to a deal ahead of a critical week for negotiations over tying immigration and border policy changes to the emergency aid package that will provide funding for Ukraine and Israel before lawmakers leave town for the holidays.

Republican Sen. James Lankford and Democratic Sen. Chris Murphy, who are leading the immigration and border negotiations, said in separate interviews on Sunday that talks are ongoing between the two sides.

“We are still in the room trying to deal with Republican demands,” Murphy said on NBC’s “Meet the Press.” “We’re not going to put Donald Trump’s immigration policies into statute. … It would be bad for the country. But, we do need to do something to try and resolve this crisis at the border.”

Casting this point in negotiations as “one of the most dangerous moments” in American history, Murphy warned in stark terms about the national security implications of not reaching a deal.

“Vladimir Putin is delighting right now in Republicans’ insistence that we get a deal on immigration reform, and if we don’t, then they are going to allow Vladimir Putin to march into Ukraine and perhaps into Europe,” the Connecticut Democrat said on NBC.

Later Sunday, the White House announced President Joe Biden will host Ukrainian President Volodymyr Zelensky on Tuesday. “The leaders will discuss Ukraine’s urgent needs and the vital importance of the United States’ continued support at this critical moment,” press secretary Karine Jean-Pierre said in a statement.

Senate Majority Leader Chuck Schumer and Minority Leader Mitch McConnell have invited Zelensky to speak at an all-senators meeting on Tuesday morning, according to a Senate leadership aide. House Speaker Mike Johnson will also meet with Zelensky at the Capitol that day, the Republican’s office said on Sunday.

News of Zelensky’s trip to Washington received pushback from some Republicans in Congress, including Sen. J.D. Vance of Ohio, who tweeted: “In the midst of a historic border crisis, Zelensky will come to Washington and demand that the Congress care more about his border than our own.”

The president sent a clear message to lawmakers last week that he’s open to striking a compromise with Republicans on border security. While both sides of the aisle have expressed an openness to reaching a deal, the two sides still seem no closer to doing so. With House Republicans demanding that the Senate-negotiated deal stick as close as possible to the House-passed border bill, HR 2, many Democrats have said that it’s a nonstarter.

But Lankford, who has remained upbeat throughout the talks, expressed optimism that the negotiators have come a long way from when they started, even as they are mired in a political “push and pull.”

“We’ve come a long way. It’s time to be able to finish this and make a decision and do what we can do to be able to help the nation. We can’t do everything on the border, but we can do the things that actually begin to control the border so that the United States is in control of our boundaries, not the cartels,” the Oklahoma Republican said on CBS’ “Face the Nation.”

“This started with the Biden administration saying we need to do a national security package that has Israel, Ukraine, Taiwan and the border,” Lankford continued. “Right now, the push and pull is really a political push and pull rather than it is anything else.”

White House budget director Shalanda Young, meanwhile, indicated in a separate interview on CBS Sunday that a deal was still possible, but warned that demands without compromise would tank negotiations.

“You can’t have everything your way in a negotiation. Democrats and Republicans have to vote for this bill. So I agree it’s time to cut a deal that both sides can agree to,” Young said.

If Congress leaves town for the holidays without reaching a deal, the White House will have to make tough choices about supplying allies such as Ukraine at the potential expense of US military readiness. Top Biden administration officials have been sounding the alarm for weeks about funding for Ukraine running dry and the potential consequences.

Murphy, the lead Democratic negotiator, also outlined in broad strokes what he sees a potential middle ground for the package.

“We don’t want to shut off the United States of America to people who are coming here to be rescued from dangerous, miserable, circumstances in which their life is in jeopardy,” Murphy said. “We’re not going to support anything that shuts down the border completely to people who legitimately are coming here to have their lives rescued. But, we are willing to talk about tightening some of the rules so that you don’t have ten thousand people arriving a day.”

This story has been updated with additional developments.

CNN’s Morgan Rimmer and Melanie Zanona contributed to this story.