I had a contractor out to do work without an estimate and received a bill for almost $20,000 demanding immediate payment

In Ohio, under the Consumer Sales Practices Act, a contractor must either give you a written estimate for the work ahead of time (which must be binding on them for five days), or give you a written notice that you have the right to receive a written or oral estimate if you choose. If the contractor gives you the notice, it should allows you to initial next to which kind of estimate you want.

Additionaly, the contractor must give the homeowner a written agreement, and also an estimated completion date in writing.

Based on these facts, it is possible that you could rescind the contract under the Home Sales Solicitation Act. 

Your question is a little fact-spcific and would require more information in order to tell you whether you can rescind the contract totally.