Ted Cruz has had a massive advantage over Trump in that the media will not do anything to expose his lies because it hurts Trump. It allowed him to lie with impunity for a long time. But like more moral flaws eventually Lyin’ Ted was exposed.
If you look beyond the Cruz-Trump interaction, you will find that every tweet about someone Trump does not like or is at odds with begins with a pejorative, from Saudi princes who were business partners to other political candidates.
Add to that 40% of Americans getting their 'news' from twitter and Facebook (the backyard fence of journalism, the one thing lower than tabloids for gossip), and the ease with which something gets retweeted or reposted, the pejorative spread through repetitive use more than substantiation. But if people hear the sky is green and the grass is blue long enough, they will believe it.
Tweets about foreign policy would definitely be interesting under a Trump administration, even if this isn't the best time in our economic history to be engaged in global warfare.