If you push the employer on it and lose the job for your efforts, you're still not getting anything. The result is the same if you pay the self-employment taxes and get laid off later anyways for whatever reason.
I think the taxes are based on *projected* earnings for the year. So if the job goes away partway through the year, you'll most like get a refund, I would think.
It's sounding like you've already made up you might to fight for the unemployment payments. Go git 'em, then.
We'll be here for you.