Well, that's one of the problems with the MTA: it's not technically under the direct control of any individual elected official. The MTA is an independent agency governed by a board that consists of five members appointed by the governor of New York State, four by the mayor of New York City, and three by county executives on Long Island and Westchester.
If the MTA were simply a city agency for which the mayor was directly responsible, it would be possible to channel voter anger (and there's plenty of voter anger, by the way) into action. But it's the governor who really has the most control, and he's responsible to a wide swath of voters outside the New York City region (who tend to want less spent on the MTA in any case). Plus many voters don't really understand how the MTA is structured, and elected officials can hide behind this independent-agency arrangement.