I am on COBRA also. The information I have is that if you are deemed to be disabled (usually by your doctor) then you are eligible for your insurance until you are covered by Medicare. I just received information from my insurance company that stated this information.

Also, I have been told that if you get your new insurance before getting off your old policy then they have to accept you and cover your pre-existing problems although they may have a time lag such as 1 month or so that they don't cover the pre-existing medical condition.