I don't know if the rules have changed with Obama Care, but back in the day when COBRA was the only option, you could easily get away without paying for insurance for those 4 months while still being covered if you needed it. Here is how:
When you lose your coverage, you then get three months before you have to decide about COBRA coverage. By the 90-day mark, say "yes" to COBRA and fill out the paperwork. You get six weeks to pay, but you will owe the entire retro-active insurance, which will be at least three months worth of premiums. By the time you have to send the money, you will be covered by your new job, so you don't actually send the money, and your option lapses.
Obviously this works best if you don't actually need insurance during that gap in time. But it allows you to effectively decide after the fact whether you really needed insurance - kind of the opposite of the idea of insurance. If you end up having an expensive medical problem during that gap, you are covered but will have to pay the whole amount of the premiums. At that point, you decide which is more expensive, medical bills or three months of premiums.