New York State (and all the rest) really needs to follow the example of Nebraska and get rid of the State Senate. A bicameral legislature makes sense on a national level (the houses represent different political constructs-- people vs. states), the houses have different jobs (treaties, approving appointees, originating spending legislation, impeachment and conviction, etc.) and having two houses slows the pace of change.
A state needs to be much more nimble in its legislating capacity. Each state is directly competing with each of the others for jobs, residents, tourists, and tax revenues. While nations compete as well, the competition is muted by legal and de facto barriers such as borders and language.
The powers of the national government are a lot scarier than that of the state, so the deliberative nature of a bicameral legislature is called for. A state can't declare war, approve treaties or move to amend the Constitution (without the backing of the other states), so deliberation is not imperative.
A bicameral legislature stalls meritorious legislation and obfuscates the guilty parties. Senators can point the finger at the Assembly; Assembly members can point fingers a the Senate. Both houses can pass different versions of popular and meritorious bills, and then let them die in conference committee. Members can chalk up politically popular votes with no fear that legislation hostile to their powerful special interest backers will not pass.