As asylum seekers have made their way across the country, often by the busloads to Democratic-leaning cities as part of Texas Gov. Greg Abbott's program, they have strained the resources and political tolerance of areas that will be vital to Biden's re-election chances.

"It's gotten to the point where, in a way, everybody's back is against the wall," said Sen. Michael Bennet, a Colorado Democrat. "I'm not talking about politically, I mean, substantively, these are challenges that the country can't ignore."

Bennet was joined at the Capitol on Thursday by Denver Mayor Mike Johnston, a Democrat who told reporters that the recent influx of migrants has caused "a humanitarian crisis and a fiscal crisis unlike anything we've seen in the last 25 years."

Democrats in Congress are split on the merits of the Senate package. Progressive and Hispanic lawmakers decry changes that would toughen the process for claiming asylum in the United States. Still, many Democrats say that Johnson's resistance to bipartisan compromise shows that Republicans aren't serious about solving the problems at the border.

"They basically want to make sure that the situation is as chaotic as possible so that they can win elections in November," said Rep. Joaquin Castro, a Texas Democrat. "That is their strategy. It's not a sincere attempt to do something about what's going on at the border."

Senate Republican Leader Mitch McConnell, meanwhile, has been strongly making the case for the deal. He's told fellow Republicans that the border package, which he insisted be paired with Biden's $110 billion request for war aid for Ukraine, Israel and other national security priorities, is a rare opportunity to get stronger policies through Congress.

The proposal crafted by the Senate would toughen the asylum process with a goal of cutting the number of migrants who come to the southern border to make an asylum claim.

Negotiators have worked on some policies intended to aid immigrants. The plan could include a pathway to citizenship for Afghans who came during the U.S. withdrawal from their country, along with work permits for migrants who enter the asylum system, according to two people familiar with the talks who were granted anonymity to discuss the private negotiations.

But the package will mostly leave out broad immigration changes, like protections for immigrants who entered the U.S. illegally as children, that have been foundational in previous Senate bills.

"It will be by far the most conservative border security bill in four decades," said Oklahoma Sen. James Lankford, the lead GOP negotiator.

Lankford and other Senate Republicans have urged their House colleagues to remain open-minded. They argue that the changes would actually pave the way for Trump to implement his border agenda if he wins the election. Lankford has also said that the legislation would not dramatically reduce the number of migrants at the border for months — a tacit signal that border security could remain a top issue through the election.

Still, Johnson has argued that a hardline House bill, H.R. 2 which passed the chamber in May without a single Democratic vote, is the solution to America's border woes. It would create a sweeping system intended to bottle up illegal immigration.

Johnson has also made clear that he has been speaking regularly with Trump.

"We're not playing politics with this, we're demanding real, transformative policy change," Johnson said this week.

Even beyond Trump, Johnson is dealing with far-right House members who are furious over his willingness to work with Democrats to pass legislation. Rep. Marjorie Taylor Greene, a close Trump ally, has threatened to trigger a motion to oust Johnson if he brings a border bill with Ukraine aid to the House floor.

Greene this week said Trump is backing the House conservatives' plan because "it brings back all of his strong border policies." In December, she said that passing bipartisan border legislation would only give Biden an opportunity to tout the legislation on the campaign trail.

"I've been telling everyone that President Trump is the leader of the Republican Party," Greene said. "That decisive victory in Iowa should be the shot across the bow to every single Republican that's elected."

Despite the pressure, Johnson signaled some support for the legislative push after a meeting this week at the White House, calling the talks "productive." But what he does next remains to be seen.

Rep. Jim Himes, D-Conn, left the White House meeting worried that a direct plan of action had not been discussed.

"We've got to figure out how to put the leaders in a position to walk over some broken glass, because whatever deal is passed is going to make a lot of people unhappy," Himes said.