Unemployed workers have raced against time to take advantage of the government’s 65 percent subsidy on COBRA health insurance premiums. But it is only a matter of time until this subsidy ends. Although there is no expiration date set, they will not last forever. Just like Cobra health insurance that only lasts 18 months. It is during this time that members of Cobra are supposed to find a new medical plan. Not after the Cobra coverage has expired, as most people wait to do and find themselves with a lapse in coverage.