I do believe, unless it has changed due to ACA, if you previously had insurance at say your regional or corporate job, once your former employer sends you the COBRA election paperwork, you then have 60 days to respond. if something happens between now and then, the coverage should be retroactive, you just need to pay the COBRA fees for that time. So at least that gives you 60 days of coverage. So basically you get 60 days for free if nothing happens.
Take vacation if you have it that extends into your start date at a new carrier, then give your two weeks notice while still on your previous company’s benefits. You may just end up not being covered for a few weeks and you can possibly get a catastrophic policy if they have those anymore with the ACA.