"Defeatist" is a favorite term of the reality-allergic.
As long as anti-illegal-immigration measures don't personally inconvenience the population at large, they are popular. Once they begin to hit ordinary folks, they will quickly grow unpopular. When they're expensive and unpopular, they have a shelf life of hours at best.
You'd have to jail a sizable percentage of the border state population to make a large dent. And you'd also inevitably hit a lot of American citizens who work off the books for cash. Yup. Great way to win friends and influence people.