DEMING, N.M. — Along a barren county fairground in this sleepy desert city sits a nondescript building that illustrates the depths of the nation's migrant crisis — and the heights to which small town America can rise.

Over the last several weeks, U.S. authorities, unable to house a surge of asylum-seekers at the border, have dropped off thousands of immigrants in this city, one of the poorest municipalities in one of the nation's poorest states.

The migrants, mostly Central American families, have arrived by the busloads to find a shelter that has become the focal point of tiny Deming.

The fire department has set up shop at the shelter's intake facility to help deal with crises. Volunteers show up in droves to lend a hand. And some churchgoers have even gone so far as to open up their homes to the migrants.

Dealing with a crush of new arrivals without federal assistance, this city of 14,000 is marshaling all of its resources to cope with the crushing weight placed on its shoulders, local officials say.

"It's been one of the best things I've done as a firefighter in all my career," said Deming Fire Department Chief Raul Mercado.

Deming is not the only city in America grappling with a weekly deluge of undocumented immigrants left at bus station depots and elsewhere by the federal government.

Since the number of immigrant families seeking asylum reached record highs earlier this year, the Department of Homeland Security has begun busing or flying immigrants from areas on the border where they enter to other towns deemed able to accommodate the overflowing populations. For example, Del Rio, Texas, and San Diego have also begun taking in immigrants who arrive in the Rio Grande Valley.

Migrant families are housed at the Deming shelter until they can be bused or flown to an American sponsoring them while they await an asylum hearing, usually after no more than two days at the facility.

"The phrase we like to use is, it's an unfunded federal mandate that's been placed upon our state," said Cullen Combs, the emergency manager in nearby Dona Ana County, New Mexico.

"I have a lot of personal thoughts about it, but when I see a mother with a child who's having a seizure because they have a 103 temperature, that's going to hit you," Combs said. "And that's something that, we as Americans, we're just, we're going to have an outpouring of being able to help these folks."

Last week, a month after Deming first began receiving the migrants, New Mexico Gov. Michelle Lujan Grisham, a Democrat, sued the directors of DHS, ICE and Border Patrol for what she called the federal government's "indiscriminate practice of releasing migrants in communities in the state's borderland area."

Grisham is seeking reimbursement for the emergency funding New Mexico has given governments in Deming and Las Cruces, as well as an injunction forcing the Trump administration to abide by the Safe Release policy.