After all the election animus (”You are the biggest liar,””Lyin’ Ted,””The Bible held high, then he puts it down and he lies.”), I can’t imagine that the President would nominate the TX Senator.
I doubt President Trump was so insecure to have taken it personally. He understands politics is a street brawl and Ted Cruz put up a fight. President Trump respected that and in turn, Senator Cruz has become one of President Trump's staunchest allies.