Answer: The reason the COBRA option is so expensive is because your employer was previously subsidizing it. Once your employment ceases you are responsible for the entire premium. Depending on the type of plan you had and how heavily your employer was subsidizing it, you can often end up with a hefty premium. So, no your employer is not taking a part of your COBRA premium but neither are they contributing to the costs any longer, hence the big increase.

Taking COBRA can be a good idea in a couple of different circumstances: first if you do not have any other options due to a pre-existing health condition that would render you ineligible for individual coverage; second if, like you, you have another plan lined up for a future date. I would add that you do not need to elect to take COBRA until near to the end of a 63 day period following your employment termination and I would only take the COBRA option if you have had any claims during that period or if your new plan starts after the 63 day period ends. Incidentally I would not recommend taking short term coverage during this time even though it would be considerably less expensive. If you do it would affect your eligibility for HIPAA (guaranteed continuation coverage once COBRA ceases).