Libel against a public figure has a high bar in this country, but just filing the suit would go a long way toward defusing this. It probably wouldn’t even really get off the ground for several months. In the meantime, if Cruz became President he could always drop the suit because he “has to spend all his time attending to the people’s business, blah, blah, blah.”
The only reason not to file a suit is if he knows he couldn’t withstand discovery.
This will fade quickly, if Cruz sues it will dominate the news cycle.