"Ya me cansé"

"Ya me cansé"
 

I heard a U.S. news reporter interpret this now-famous phrase (the reporter spoke it without the required final accent) as "I'm tired." Being the preterite tense, shouldn't it be more accurately something like "I got tired [of it]"?
And what about the Ya? Could it be something like "I'm already tired [of it]" even though that would be present and not preterite?

Yes, I agree.

Ya me cansé [Latin America] = Ya me he cansado [Spain mostly] = Ya estoy cansado.

For me, the differences respect to nuances are similar between both languages. It expresses disagreement and discomfort.

A pleasure.

In the context where it was said (a long press conference by a high-profile bureaucrat that had been standing a long while talking about a very delicate matter and answering repetitive questions of reporters) it can be read as "I'm tired now".
He was asking to cut the session at that moment, as the most important issues had already been addressed.
(May I mention that this was felt as a disrespectful attitude, and that's why it made it to international press.)

Yes, it's really making the rounds. Something akin to what that oil company spokesman said after the gigantic spill messed up the entire Gulf coast, "I'd like to get my life back."