FYI It is about 1530 miles from Jacksonville, NC to Laredo TX - one of several border towns in TX much closer than El Paso. That's about 25 hours driving at 60 MPH without stops except for gas. He left Jacksonville sometime Thurs night (it was before 4AM Fri morning if the wife is to be believed). If he was driving, even if he stopped and slept a few hours, he was in Mexico by sunrise Sunday morning. If he was on a bus, and IF he was in Shreveport Saturday at midnight he could easily have been in Mexico by bus by midnight Sunday - its only 578 miles from Shreveport to Laredo. I don't think he would have gone to El Paso when Laredo, McAllen and Eagle Pass are all closer to Shreveport.
IF was headed to Mexico, he would be there by now. And if he is driving his own vehicle all he had to do was head off into the Texas/Mexico border area on any one of hundreds of dirt roads and drive straight to the border and cross. Border patrol isn't looking for people sneaking INTO Mexico. They won't find his vehicle for days and it may even get stolen before LE can find it.
Otherwise he took a Greyhound bus and A - got off in Laredo or McAllen and walked or rode one of the little tourist trams into Mexico. Or B - took one of the 20 or 30 independent bus company's buses that transport Mexicans legally into and out of the US every day from Shreveport, or Dallas and rode in to Mexico with the other travelers returning from the US. He doesn't need a passport or an ID to get IN to Mexico...just to get back OUT. They barely look at you OR your ID when you enter Mexico from the US and I'll betcha has a Mexican birth certificate - if so, that is ALL HE NEEDS - IF he is asked for any ID at the border at all. He is a native Mexican Spanish speaker - he wouldn't get a second glance riding on one of the Mexican bus lines or walking across at the border on a weekend. He'd blend right in.
LE didn't issue the warrant until Sat AM - could easily have been in Mexico before any BOLO went out nationwide.