COLOR: blue; ; If our group insurance has Medicare as a secondary payer, (because I was in a trial working period and disabled) and we switch to cobra, because of fewer hours, does Medicare become primary or stay secondary? And can cobra go back and demand all money spent in the Medical bills, saying they should have been the secondary payer. This is happening to us, what can we do?? COLOR: blue; A: Once you are entitled to Medicare you are no longer allowed to continue on the employer ‘s group health plan (COBRA). If you have a spouse or any dependants, they may take advantage of COBRA, but you will not. You are not able to have both Medicare and COBRA. You may have to submit all bills to Medicare.