Challenges to Cruz will be at the state level, so that means 50 of them, at the very least. However, if multiple Democrats sue over Cruz's eligibility in each state, we are now looking at hundreds of suits to be adjudicated. Then AFTER that (which I would think is a multi-year process with stalling and delays by Dems) it could be elevated up the chain of appeals courts.
That is a good summary. The Dems would turn Cruz anyway but loose. It would be a legal and media circus, and no fun for our side at all.