EL PASO, Texas (NewsNation) — The Biden administration is finalizing its response to the anticipated end of the controversial but key piece of border policy known as Title 42.

In a last-ditch written appeal to the Supreme Court, several Republican-led states argued that increased numbers of migrants would take a toll on public services such as law enforcement and health care and warned of an “unprecedented calamity” at the southern border.

Supreme Court Chief Justice John Roberts on Monday granted a stay pending further order, asking the administration of President Joe Biden to respond by 5 p.m. Tuesday. That’s just hours before restrictions are slated to expire on Wednesday.

The Department of Homeland Security, which is responsible for enforcing border security, acknowledged Roberts’ order — and also said the agency would continue “preparations to manage the border in a safe, orderly, and humane way when the Title 42 public health order lifts.”

Migrants have been denied rights to seek asylum under U.S. and international law 2.5 million times since March 2020 on grounds of preventing the spread of COVID-19 under a public-health rule called Title 42.

The decision on what comes next is going down to the wire, as pressure builds in communities along both sides of the southwestern U.S. border.

This comes as thousands of migrants are sleeping in the streets in El Paso in near-freezing temperatures because shelters and holding facilities are packed.

Mayor Oscar Leeser warned Monday that shelters across the border in Ciudad Juárez are packed to capacity with an estimated 20,000 migrants who are prepared to cross into the U.S.

Leeser issued an emergency declaration Saturday after a crushing number of migrants arrived in the city. He predicts 5,000 or more migrants could arrive in the community daily after Title 42 is lifted. Because of that, 400 Texas National Guard members just arrived in El Paso to help process migrants and scare off more crossings.

Despite the court stay Monday, the City of El Paso rushed to expand its ability to accommodate more migrants by converting large buildings into shelters, as the Red Cross brings in 10,000 cots.

Local officials also say they hope to relieve pressure on local shelters by chartering buses to other large cities in Texas or nearby states, bringing migrants a step closer to relatives and sponsors in coordination with nonprofit groups.

“We will continue to be prepared for whatever is coming through,” Leeser said.

Border patrol agents encountered more than 2.3 million undocumented migrants along the U.S.-Mexico border during the 2022 fiscal year, according to Customs and Border Protection data, compared to the previous record of more than 1.7 million encounters during the 2021 fiscal year.

While it’s unclear how much longer Title 42 will stay in place, border communities are still dealing with the record-breaking surge in migrants.

Many leaders, like Texas Gov. Gregg Abbott, are glad Title 42 will remain in place for now.

Meanwhile, the Department of Homeland Security, which is responsible for enforcing border security, acknowledged Roberts’ order — and also said the agency would continue “preparations to manage the border in a safe, orderly, and humane way when the Title 42 public health order lifts.” They’re also urging Congress to use this extra time to get funds and resources in place.

For its part, the Biden administration says it will be legally required to end Title 42 at some point despite the calls to leave it in place. It’s asking Congress for $3.5 billion so DHS can better help Border Patrol agents and communities.

The Associated Press contributed to this report.