I can see two theories for why Jeb said what he said.
1) Jeb wants to argue that he favors a secure border. If that’s going to happen he also logically has to stop visa overstays — 40% of the illegal population, as he says — in addition to policing the Rio Grande. Otherwise there’s a big hole in the immigration system.
2) Visa overstays are less likely to be Latinos than border-crossers. Bush needs to win over Latinos, but he also needs to show he’s not a total wimp on immigration. Solution: crack down on those illegals who are least likely to be Latino! A visa crackdown might even appeal to Latinos — a possibility that was driven home to me during my quixotic ** 2010 Senate run when Latino voters complained about all the focus on border-crossers while visa overstayers were home free. In effect — actually, in so many words — the argument was: ‘You’re cracking down on brown people while you leave all those Irish “tourists” alone.’ Not an unreasonable point. Bush’s anti-overstayer stand might have seemed like a chance to appear tough while maintaining — even deepening — his pander to Latinos. Unfortunately for him, Presente.org wasn’t about to pass up an opportunity to ethnicize opposition to any kind of deportation.