Ruben Garcia of Annunciation House said Thursday that nonprofit groups have had to expand their services because more people are crossing the border and the government doesn't have the space to hold them.
Garcia estimates his organization spends $150,000 a month renting rooms because there isn't enough shelter space. More than 500 people arrived on Wednesday.
Sister Norma Pimentel of Catholic Charities in Texas' Rio Grande Valley says her respite center is also serving more people than usual.
The Department of Homeland Security has come under harsh scrutiny after the second death of a migrant child in U.S. custody in three weeks.
A DHS spokeswoman says the U.S. is in "an immigration crisis."