Cut how? Does the budget come from the Governors office? (Hint: It's probably in your 2nd grade Textbook)
So he vetoes the budget. Then what? They send him another one. So he vetoes that. Then what?
He's trapped. The D's know they can't lose because of the jerrymander, and he can't win. He must balance the budget, eventually, assuming the D's don't blink, which, since they can't lose, they have little reason to blink, he must sign one eventually.
Show me a logical way out of this and I'll concede the point.
Ummm... YES, it does. The governor is the one who proposes the butdget. You better lose that second grade textbook and start looking at the state constitution instead.
So he vetoes the budget. Then what? They send him another one.
While you are reading up on the duties of government officials, pay specific attention to the words "line item veto," a power the governor currently has. That should show you how ridiculous it is to say that "he is trapped."