flc - that's it! You've solved political gridlock! Elect state officials who can fix it! Why didn't ANYBODY ELSE IN THE COUNTRY think of that?
In all seriousness (Cuomo's term being the exception, for the most part), New York has been governed by "three men in a room," the three men being the Governor, Senate President, and Speaker of the Assembly. New York had the same Senate President and Speaker for decades under Joe Bruno and Sheldon Silver. Bruno was booted a few years ago for corruption charges but Silver is still firmly entrenched. Cuomo has done a much better job of bringing a level of transparency to state politics, but even his most notable victory (gay marriage) was won behind a lot of closed door meetings with four on-the-fence Republicans who ultimately voted in favor of the bill.
Even as recently as three summers ago, Republicans went for a power grab in the Senate by convincing one Democrat legislator (Hiram Monserrate and Pedro Espada) to change sides while naming Dean Skelos the "new" President of the Senate. Espada was notorious for hiding campaign funds and contributions, and Monserrate was under investigation at the time for domestic assault (hit his girlfriend in the face with a water glass - apparently, he yelled "You want some water?! Here's your water!!! haha). Democratic legislators left the state and then-Governor Paterson was essentially helpless to do anything, not that he ever did much anyway.
Anyway, most NY legislators are or were firmly entrenched. My assemblyman and senator, for example, have both been in office since before I was born and know how to work the Albany political machine well enough to stay in office without any real challenge. One party is typically in control for long periods of time, so when the other party comes into power, like the Republicans did in the last election, they come down hard on Democratic districts by drawing horrible districts like these to consolidate power.