The state has vowed to assist the president in his efforts to revamp immigration. But Texas' biggest cities and school districts are more reluctant to help.
The warning was issued because of "increasingly frequent gun battles" and the discovery of "improvised explosive devices (IEDs)."
Officials conducted exercises with Black Hawk and Chinook helicopters, and military trucks, highlighting tactical strength.
Texas Gov. Greg Abbott is sending helicopters and hundreds more soldiers from bases in Houston and Fort Worth to the U.S.-Mexico border in the Rio Grande Valley.
A new bill filed in the Texas Senate would create a new Homeland Security division within the Texas Department of Public Safety.
The U.S. government is asking people to avoid traveling to certain areas of the Texas-Mexico border due to security concerns.
U.S. officials have put several Mexican border towns near Texas under the highest-level travel advisory amid gun battles, kidnappings and IEDs in the area.