But unlike last summer's crisis of children and families arriving from Central America, lawmakers aren't quick to call on this current group of refugees to go home.

From October 2014 to June 2015, about 18,520 Cubans have sought entry to the United States through Texas' Laredo field office of U.S. Customs and Border Protection, which includes ports from Del Rio to Brownsville. That's compared to the 18,240 unaccompanied minors that were caught or surrendered to U.S. Border Patrol in the Rio Grande Valley from October 2014 through July of this year, according to CBP statistics.

If current trend holds, the number of Cubans seeking entry through Laredo will be about 24,700 this fiscal year. That's about 60 percent more than 2014's 15,600 and nearly twice as many as 2013's 12,445.