Cruz was speaking of borders and illegal immigration last night. He supports legal immigration to include H1B visas. I disagree with him on that, but that wasn’t discussed last night.
Even Trump supports legal immigration. If you listened to Trump last night, he talked again about how most of the people he would deport would come right back in with a guest worker permit. So even Trump's plan wouldn't significantly reduce the competition for jobs or affect the downward pressure on wages.
With regard to H1B's both Trump and Cruz have talked about the need to crack down on employers that are abusing the system by replacing existing American employees with lower paid H1B employees. But neither of them is suggesting eliminating the H1B program entirely.
It is one thing to oppose illegal immigration - we should oppose it vigorously and attack it with all of the tools available. But if we also reflexively oppose legal immigration, we make it easy for the left to paint conservatives as racists, nativists and xenophobes. Improve the legal immigration system. Make sure we are allowing in people who will help make America better, not the ones who want to change it or just suckle at the government teat. Make sure immigration is not used as a way to hold down wages for American citizens. And then make the process easier for those people who qualify.