Yes, COBRA is 18 months ... at least initially. My 18 months is up at the end of July. However, there is an 18 month-extension of COBRA under a law passed by Gov Paterson in Nov 2009 -
State Continuation Coverage Extension to 36 Months. However, this does not apply to self-funded insurance plans and unfortunately my employer is self-insured.
To qualify for Medicaid, you need to be practically destitute. Monthly income needs to be less than $707 and I think the limit for savings is about $20,000. There is also Family Health Plus, there the weekly income must be $208 or less.
If you qualify for Healthy NY, the premium will likely be a lot less than what you are now paying in COBRA. And you don't have to exhaust your COBRA to switch to Healthy NY. Of course there are a lot of limitations in coverage.