There would (should?) still need a 2/3rd majority to vote yes again, but you make a fair point. Especially given our current federal government.

Yes and no. Then the legislators could then pass all the bills at the end of a session and skip the governors ability to veto anything, which harms the separation of power that should be happening now. Really, just make it so the legislators can override a veto no matter when it was vetoed.

Oh hey look. Bribery.