I've finally found the term for my job status: Underemployed. I wrote about it today on WalletPop.com. Go here for story.
It's a government term that means I'm not classified as unemployed, but seek work and can't find it and thus work part-time. It also applies to people with full-time jobs who have had their work hours cut to 35 hours or less per week. As I've written about many times on Unemployed Dad, I have about six part-time jobs of varying infrequency to help pay the bills. None offer health care.
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