@Aprendo: The meaning of "me canso ganso" has been explained in the link Rusty provided.
It just means "estoy seguro". In this precise case of the Mexican president sentence, it means "I'll make sure that it happens".
The phrase became viral because it's rather uncomfortable to hear a politician use slang during a formal speech, and because it's old slang; I'm sure many young people hadn't ever heard it before. And it caused some sort of outrage because the topic of the new airport for Mexico City has been quite controversial from the very start and he has vowed to build his own personal vision of it.
By the way, Germán Valdés was a successful comedian who was very popular and is still admired; I'm not surprised that this joke became a common phrase. He liked plays on words, double meaning, rhymes, sarcasm and nonsensical sentences (like the zancudo thing).
Anyway, you may find many expressions in (old) Mexican slang that don't make sense but rhyme.
