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As thousands of migrants cross from Mexico into South Texas, homeless shelters and missions are over capacity and overwhelmed due to a lack of government preparation, a mission director told Fox News.

"The city wasn't prepared for it, and I think they kind of tried to downplay the seriousness of it just to not worry people," said Nicole Reulet, a director for Rescue Mission of El Paso. "It is an emergency."

The area near El Paso faced a three-day average of nearly 2,500 crossings over the weekend, according to Border Patrol. The city has never dealt with such a large influx of migrants before, according to El Paso Deputy City Manager Mario D’Agostino, who called the record crossings "unsustainable."

WATCH: El PASO SHELTER DIRECTOR OVERWHELMED BY RECORD MIGRANT CROSSINGS

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"There needs to be a bigger plan than just depending on shelters and the welcome centers," Reulet told Fox News. "It worked in the beginning, but it's starting to get strained and the weight of that is starting to show."

"Our capacity is 190 and we're currently at 260," she continued.

Migrant women and children sitting

Migrant women and children in a shared room at Rescue Mission of El Paso. (Fox News Digital / Jon Michael Raasch)

Shelters, churches and missions all over El Paso are at full capacity, forcing some migrants to sleep on the streets, in the airport or wherever they can protect themselves from the winter cold, according to Reulet. Migrants arriving in El Paso have used the local airport as a shelter since mid-September, an El Paso Police sergeant previously told Fox News.

"We have people sleeping on the floor, and there's no floor left," Reulet said. "It's at a point where resources are scarce. There's not enough room."

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Homeland Security Secretary Alejandro Mayorkas visited El Paso earlier this week for a briefing with local Customs and Border Protection officials. Also this week, El Paso Mayor Oscar Leeser decided not to declare a state of emergency, which would enable the city to receive state and federal funds to help alleviate the pressure. 

"It's unfair that we have the potential to find the funding and find the space and find the resources, but because of politics or because of whatever, we're not pursuing that," Reulet said.

Nicole Reulet sitting in her office

Nicole Reulet, marketing director of Rescue Mission of El Paso, said the shelter is far over capacity. (Fox News Digital / Jon Michael Raasch)

"The reason why shelters or churches have gone 105% is because they have the heart behind that," Reulet continued. "With politics, it's a little bit more separated, but it's reaching a point where it's almost cruel."

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Communication between city officials and the shelters has been strained and disorganized, Reulet told Fox News. 

"Someone needs to take action and take leadership and make a plan," she said. "Now is the 11th hour, and we really need to prepare before Title 42 gets lifted."

Migrants at the El Paso border

More than a thousand migrants awaiting entry into the United States from Juarez, Mexico. (Fox News Digital / Jon Michael Raasch)

Title 42, a health protocol that enables the government to quickly expel migrants, is set to end on Dec. 21. Federal officials expect migrant crossings will increase significantly as a result. 

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"It's concerning that we haven't been better set up for this," Reulet said. 

"If there's no leadership, if nothing changes, then it's just going to keep going because the shelters are at capacity," she told Fox News. "All of us are at capacity."

To watch the full interview with Nicole Reulet, click here.

Ramiro Vargas contributed to this report.