Under a bridge connecting the U.S. with Mexico, dozens of migrant families cram into a makeshift camp set up by U.S. Customs and Border Protection. The families are there because permanent processing facilities have run out of room.

Seven hundred miles east, busload after busload of weary, bedraggled migrants crowd into the Catholic Charities Humanitarian Respite Center in McAllen, Texas. Organizers there are used to handling 200 to 300 migrants a day. Lately, the migrants have been arriving at a clip of around 800 a day, overflowing the respite center and straining city resources.

"It's staggering," McAllen City Manager Roy Rodriguez said. "Really, we've never seen anything like this before."

Along the Texas border with Mexico – from El Paso to Eagle Pass to the Rio Grande Valley – masses of migrants have been crossing the border in unprecedented numbers, overwhelming federal holding facilities and sending local leaders and volunteers scrambling to deal with the relentless waves of people.