The incoming congresswoman of the Texas border city of El Paso is warning of an imminent "crisis" as local officials and charities scramble to accommodate at least 1,600 migrants dropped off there by federal authorities in recent days.

Representative-elect Veronica Escobar, a Democrat, told CBS News, "We have these teams coming in to play in our Sun Bowl this weekend and the hotels are booked," referring to the college football game El Paso has hosted since 1935. "We're facing a real crisis coming up … to find places for all of these (migrant) families."

Escobar said migrants who can't be housed in shelters have been staying in hotel rooms paid by Annunciation House, the non-profit spearheading the efforts to house and feed them. But, she said, if U.S. Immigration and Customs Enforcement (ICE) continues releasing large numbers of migrants, the El Paso community will struggle to find places for them because many hotels have been booked by people attending Monday's game.

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Escobar added it's already been "very, very difficult and very challenging" to put up the migrants dropped off by ICE. And, she said, the coming hotel crunch will only make the task tougher.

In a bilingual press conference Thursday, Annunciation House Executive Director Ruben Garcia said ICE has released more than 1,600 migrants in El Paso since Sunday. He said a drop-off Wednesday of more than 500 migrants was the largest he's witnessed, and ICE released approximately 320 more Thursday.

An ICE spokesperson told CBS News the agency is releasing large numbers of migrants because of overcrowding in its holding facilities and to avoid violating Flores agreement limitations on the time families can remain detained by immigration authorities. The spokesperson added that ICE is notifying local officials and groups before conducting drop offs in El Paso, but warned that charities are informing the agency they are struggling to accommodate more migrants.

Katie Waldman, a spokesperson for the Department of Homeland Security (DHS), said the situation in El Paso stems from decisions by "activist judges."

"We are living through an immigration crisis that is in part driven by a disastrous ruling by a district court judge in the Ninth Circuit that incentives illegal alien adults to put their children in the hands of smugglers and traffickers. The Flores Settlement Agreement has created an immigration loophole that rewards parents for bringing their children with them to the United States," Waldman wrote in a statement to CBS News Friday.

Escobar called on the Trump administration to help El Paso by undertaking the "short-term" solution of investing in "family-friendly" holding facilities for migrants. "This really is a federal obligation and the federal government needs to step in and build some temporary housing facilities, in the way that they did in 2016," she said. "That needs to happen immediately."

The long-term solution, she added, is to invest heavily in the "Northern Triangle" of Guatemala, Honduras and El Salvador to curb the region's widespread poverty and intensifying gang violence.

"We need to work with Central America and make probably some significant investments there and hopefully, through good collaboration, find some solutions to the poverty and crime that are driving thousands and thousands of people from Central America into the United States," Escobar said.

ICE's drop-offs of migrants in El Paso during the holidays, as well as the deaths of two Guatemalan children in U.S. Border Patrol custody near the city, have transformed it into a focal point of the nation's intense debate over immigration. Democrats have been fiercely critical of the Trump administration's hardline immigration agenda. Embattled DHS Secretary Kirstjen Nielsen is scheduled to visit El Paso Friday.

Although Escobar is well aware of the challenges her district is facing, she said her soon-to-be constituents will continue to welcome migrants.

"As a community, we are going to do whatever we need to do to take care of these people. They are vulnerable. They deserve compassion. And help. And support," she said. "And El Pasoans always rise to that occasion."

Escobar will join Representative-elect Sylvia Garcia next week as the first Latinas to represent Texas in Congress. Garcia's district is in the Houston area.

Escobar will fill the seat being vacated by Rep. Beto O'Rourke, who unsuccessfully challenged Republican Sen. Ted Cruz. O'Rourke is now seen as a possible contender for the Democratic presidential nomination.