An atomic weapon would weigh several tons and would be extremely difficult to smuggle from Syria or Estonia to El Paso.
Our government has concentrated on stopping the smuggling of a nuclear bomb at its source, at ports in Europe, Asia, Africa and the Middle East; at ports in South and Central America; at the Southern border of Mexico and finally at our own border. We even board ships headed toward Mexican ports.
At most official crossing points we have installed x-ray equipment and equipment that can detect nuclear particles. To protect our border between official crossing points we have areal surveillance (manned, unmanned and satellite) and ground sensors.
But most of the people complaining about nukes crossing the Mexican border really aren't concerned about nukes, they really just want to keep Mexican laborers from crossing. But the way you prevent nukes from reaching the U.S. is different than the way you stop Mexican laborers.
The fact that millions of Mexican laborers can climb over mountains, swim rivers, and trek across desserts does not mean that an eighteen wheeler can get across unnoticed.
The biggest threat of a nuclear weapon crossing the southern border is corrupt border guards. I've heard that corruption is very common regarding drug smuggling and human smuggling, but I would hope no set of guards would conspire to allow a nuke to pass through.