Of course you can negotiate but yes, they could walk away. Depends on what your bottom line is. I agree that $20 per hour is too low. So you could tell them what you told us about industry rates and what you've earned in the past.

In your situation, I'd probably ask for $35 and offer to do the first assignment prior to signing a contract for free to show them you're worth it.

It could well be that you'll cost more per hour but be quicker than they're used to?