As you can see in the linked video, I asked specifically for a name when it came to what Supreme Court Justices the candidate would pick... which I feel made sense at the time, but unfortunately the subsequent and untimely death of Antonin Scalia made that question effectively impossible for any candidate to answer. It's one thing when it's a potential vacancy; it's quite another when there's an actual vacancy on the court and whoever the candidates named would be instantly on the hot seat because the Democrats would love there to be a fight over this now. At any rate, here's Ted Cruz's written reply:
This issue is incredibly important, and the sad reality is this, Democrats, when they make Supreme Court appointments they bat almost 1000. Their appointments are liberal activists and they vote left-wing on every major case. Republicans, we bat about 500: about half the Republican nominees turn out to be total disasters. Earl Warren, Bill Brennan, John Paul Stevens, David Souter, Harry Blackmun the author of Roe vs. Wade. Every one of those was a Republican appointee. But when it comes time to nominate someone, they don’t want to spend the political capital to actually confirm a proven constitutionalist. The other Republicans in the field do not have the record to give us any reason to believe they would be any different.
The next president could get one, two, three, four Supreme Court Justices. I have spent my entire adult life fighting judicial activism, fighting to defend the Constitution. I give my word that every justice I put on the court will be a principled conservative jurist, a constitutionalist who follows the law and does not legislate from the bench, and I will be willing to spend the political capital to ensure the justices get confirmed because their task is protecting the constitutional liberties that are the very foundation of our nation.