Cruz is potentially a great American Senator, but he is not a natural born citizen. A NBC is someone who is born in country to citizen parents.
Since he is NOT Constitutionally eligible for the office, I will NEVER vote for him should he run for POTUS, but I do hope with all my natural born American heart he is made Senate majority leader.
Clearly, the Constitution doesn't mean much any more, so y'all can be just like the demonrats and do whatever you like.
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Interesting take on that subject in the following linked article. Should Senator Cruz make the decision to run his NBC will definitely be a topic of discussion. My guess is outside of some banter from both sides Senator Cruz would be sworn in as President should he get the required number of Electoral College votes.
Take care ..