The White House and U.S. Congress are racing to strike a deal that would deliver military aid to the two allied nations while discouraging illegal immigration across the U.S.-Mexico border with only a week until lawmakers depart for a Christmas break.

Republicans have refused to approve more Ukraine funding without additional measures to reduce the record number of migrants attempting to cross the U.S. border illegally, leading to a complex negotiation pairing the largely unrelated issues.

President Joe Biden, a Democrat seeking reelection in 2024, said on Wednesday that he would be willing to make significant concessions on border security as Senate Republicans rejected a Democratic aid package with $20 billion in border funding.

The White House would be open to heightening the standard for initial asylum screenings, a source familiar with the matter told Reuters, requesting anonymity to discuss the talks.

The Biden administration also would entertain some form of a "safe third country" provision that would deny asylum to migrants who pass through another country en route to the U.S., the source said.

Another possible point of agreement could be expanding a fast-track deportation process known as "expedited removal." The authority would be employed nationwide instead of its current application at the border, the source said.

A bipartisan group of senators trying to reach a deal are also discussing a numerical limitation on asylum claims, the source said. The Biden administration position on such a cap remains unclear.

White House spokesperson Angelo Fernandez Hernandez said Biden has made it clear "the border is broken" and that Congress should take action to fix it.

"The president has said he is open to compromise," he said in a statement.

The Republican-led House of Representatives is scheduled to wrap up work for the year by Dec. 14, leaving a tight window to pass legislation. The Democratic-led Senate faces a similar timeline.

With that in mind, the goal seems more to strike a top-line deal and perhaps work on the exact details of the legislative text over the break, sources said.

Democratic Senator Chris Coons said Thursday the gap between his party and Republicans remains "stubbornly large" but that he remains optimistic they can find common ground.

White House spokesperson Karine Jean-Pierre criticized Republicans during a press briefing on Thursday.

"They are playing chicken with our national security," she said. "History will remember them harshly."

Republican Senator Thom Tillis, part of the bipartisan group trying to hash out a border security compromise, told reporters on Wednesday that any proposal would have to cut illegal immigration at least by half and that he did not know if a deal could be reached before Christmas.

"We’ve got a lot more work to do," he said.