President Biden and Democrats on Capitol Hill are seriously considering Republican demands for deeply restrictive immigration policies in exchange for billions of dollars in aid for Ukraine, a move that activists say would devastate America’s obligations to welcome desperate migrants fleeing war and oppression.

Mr. Biden has said he is willing to make “significant compromises” on border security to satisfy Republicans, who will not support any more aid for Ukraine without a new crackdown on immigration.

Republicans last week blocked a $111 billion emergency spending bill, which includes about $50 billion in security assistance to Ukraine, and made a counteroffer that amounted to a Trump-era wish list for the border.

Mr. Biden has accused Republicans of holding military aid to Ukraine hostage in exchange for “an extreme Republican partisan agenda on the border.”

Here’s a look at the state of the negotiations:

What Republicans Want

Republicans have said they want to make it more difficult to gain asylum in the United States — a demand that the White House has signaled it is willing to consider.

But Republicans say that is not enough.

They also want to restore policies that would either rapidly turn people away at the border or force them to wait in Mexico until their asylum case is heard. Former President Donald J. Trump used those methods to effectively shut the border to migrants during his administration.

Republicans are seeking to expand a policy known as “expedited removal” to rapidly deport undocumented immigrants. They also want to restrict the use of an immigration policy known as humanitarian parole, which has allowed thousands of Afghans, Ukrainians and others fleeing war and violence to come to the United States.

Republicans say the overhaul is necessary to contend with crossings at the border that have surpassed 10,000 per day recently.

What the White House Would Consider

The White House has signaled that it is open to several Republican proposals, according to Biden administration officials, lawmakers in both parties and people familiar with the matter.

According to people involved in the talks, Democrats have agreed in principle to raise the standard migrants must meet when they claim they need asylum in the United States because they fear persecution in their home countries.

The White House has also said it would consider a policy similar to the Trump-era emergency rule known as Title 42, which empowered border agents to rapidly expel migrants at the border, according to Senator Thom Tillis, a North Carolina Republican who is involved in the talks.

The White House included some G.O.P. demands in the emergency funding request that Republicans blocked, such as a significant expansion of detention capacity. The bill dedicated more than $4 billion to the Department of Homeland Security to expand holding facilities at the border.

And the White House has considered the idea of reinstating a practice of detaining migrant families that cross the border together — another line item in the G.O.P.’s latest proposal.

But other Republican proposals could be difficult for the White House to accept, such as forcing migrants to remain in Mexico while their cases are being heard and restricting humanitarian parole. The White House has emphasized that it has not signed off on any of the proposals.

Karine Jean-Pierre, the White House press secretary, declined to comment on Wednesday about the specific immigration proposals being discussed in the negotiations.

“We have to find a bipartisan compromise,” Ms. Jean-Pierre said.

The Politics

The White House is facing pressure from all sides.

The southern border has been a major liability for Mr. Biden, who has not been able to stem the tide of crossings. The negotiations have only highlighted a crisis that has prompted a bipartisan backlash against Mr. Biden.

The negotiations also cut to the heart of Mr. Biden’s foreign policy. The president has promised to support Ukraine’s fight against Russian invaders for as long as it takes, and he has characterized the aid as a matter of American credibility.

President Volodymyr Zelensky of Ukraine was in Washington this week, lobbying lawmakers and warning that his country will lose the war without American support.

Senator Chuck Schumer, the majority leader, has called on Speaker Mike Johnson to keep the House in session next week so that members could have more time to negotiate.

“If Republicans are serious about getting something done on the border, why are so many in a hurry to leave?” Mr. Schumer said on Wednesday.

But pessimism was growing.

“It’s a long ways from, I think, being close to any kind of an agreement,” said Senator John Thune, Republican of South Dakota.

Progressive Democrats and immigration advocates, meanwhile, are infuriated that the White House is even considering the restrictions proposed by Republicans.

“How will they credibly be able to campaign against Trump’s immigration agenda when they are the ones leading the fight to turn it into law?” said Andrea Flores, the former director for border management at the National Security Council. “They are going against the entire party to support the most exclusionary immigration policies in over 100 years.”

Hamed Aleaziz contributed reporting.