WASHINGTON (AP) — Senate negotiators were trying to land a bipartisan border security proposal this week that could unlock Senate Republican support for Ukraine aid. But as Congress returns, House conservatives are trying to interject their own hardline immigration demands.

Senate negotiators met Monday morning as they raced to finish work on legislative text. They were hoping this week to present the details of a bipartisan bill aimed at reducing the number of migrants who travel to the southern border to apply for asylum protections in the U.S. The small group of senators has been working for months on the legislation after Republicans insisted on pairing border policy changes with supplemental funding for Ukraine, but disagreements remained.

“I am more hopeful right now, even more than I was a few days ago, that we can get something meaningful done on the border and pass the supplemental,” said Senate Majority Leader Chuck Schumer in a speech Monday. “Getting over the finish line is still not going to be easy.”

President Joe Biden’s administration has also been directly involved in the talks as the president tries to both secure support for a top foreign policy priority — funding Ukraine’s defense against Russia — and demonstrate action on a potential political weakness — his handling of the historic number of migrants seeking asylum at the U.S. border with Mexico.

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Biden has faced staunch resistance from conservatives to his $110 billion request for a package of wartime aid for Ukraine and Israel as well as other national security priorities. In the Senate, Republicans have demanded that the funding be paired with border security changes.

“The stakes here are quite high,” said Senate Republican Leader Mitch McConnell. “We have an opportunity to make the most comprehensive headway on border security in a generation.”

But in the House, conservatives have criticized any proposals that fall short of the strict border measures they passed on a party-line vote last year. And some House members aligned with Donald Trump, the former president and current Republican presidential front-runner, have suggested they would not support any bipartisan proposal — no matter the substance — if it means giving Biden a border bill to sign in an election year.

House Speaker Mike Johnson, joined by about 60 fellow House Republicans, visited a Texas border city last week to press the case that the border legislation should tack closely to what the House has already passed. Johnson said the visit only increased his resolve to ensure border policy changes are included with Ukraine funding and called the House bill a “necessary ingredient.”

Over the weekend, congressional leaders reached a separate agreement on overall spending figures for the current fiscal year as they try to pass legislation to avoid a partial government shutdown in less than two weeks. But leaders made no mention of border policies or Ukraine aid, and some conservatives in the House have pushed to use the prospect of a government shutdown as further leverage in the negotiations over border policy.

White House press secretary Karine Jean-Pierre told reporters on board Air Force One on Monday that Republican should “stop threatening to shut down the government and fulfill their basic responsibility to fund critical domestic and national security priorities., including the president’s supplemental requests. It’s time for them to act.”

The White House has continually pressed Congress to approve supplemental aid for Ukraine, warning that the U.S. cannot send any more significant amounts of military equipment without approval. A lack of U.S. support would significantly diminish Ukraine’s defenses and weaken its government.

Johnson has pointed to a deadline of providing the funding to Ukraine by February, saying that Ukrainian President Volodymyr Zelenskyy told him that was when funds would be needed during Zelenskyy’s December trip to Washington.

In the Senate, where negotiators have been plugging away at a bipartisan compromise, even the head GOP negotiator, Sen. James Lankford, has acknowledged that the final agreement will not include all of the conservative priorities.

“We’re always focused on what it would take to pass a bill through the House, the Senate and receive the president’s signature,” Sen. Kyrsten Sinema, an Arizona independent central to the negotiations, said Monday.

As talks have progressed, the White House has tried to protect humanitarian parole, which is has used to allow 30,000 people a month from Venezuela, Nicaragua, Cuba and Haiti entry into the U.S. if they have a financial sponsor and fly into the country.

Negotiators have also been grappling with how to implement a new series of border enforcement measures — many similar to those that were pursued by the Trump administration — that would be triggered if the number of daily crossings reach a certain threshold. It has proven difficult to reach agreement on what that threshold should be, according to people familiar with the talks who discussed the private negotiations on the condition of anonymity.

“We’re certainly narrowing down the issues,” Sen. Chris Murphy, who has been leading the Democratic side of the negotiation, told reporters. “We’re hopeful we’ll have something to present to our colleagues soon.”

The emerging package also faces criticism from the left, with some progressive and Hispanic lawmakers raising concerns about policy changes that would restrict a migrant’s rights to seek asylum, which offers people protection from persecution in their home countries. Immigrant advocates critical of the proposal were planning to rally in Washington this week.

As senators gird themselves to address an issue that has eluded congressional action for decades, the no. 2 Democrat, Sen. Dick Durbin of Illinois, said he was still waiting to see what the talks would produce and expressed concern about curtailing humanitarian parole for immigration. Presidential administrations have used the authority over the decades to provide urgent relief for people fleeing war.

“I don’t know what the final product will be, and I hope I can support the bill. But this process was long, long overdue,” Durbin said in a Senate floor speech.

He concluded by saying he hoped the Senate negotiation “moves us in the direction of an orderly process at our border, not being overwhelmed with numbers that are unsustainable.”

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Associated Press writer Seung Min Kim contributed.