Sue

It's not clear you really had an oral contract with this lady since it seems you never agreed on your daily fee. For a contract to be enforceable the terms need to be certain, and price is a material term.

You could sue her in Small Claims court if she refuses to pay you for the reasonable value of your services. The Latin name for this claim is "quantum meruit," and you'd get more than $20 per day, especially for a 9 hour day.

You can't expect to sue for payments you would have made if the job had been permanent, because it would be implied that there would be a trial period at the beginning of employment, and the fact that she fired you after only 1 week means it didn't work out, and she could fire you at any time for any reason, and you could quit at any time for any reason.

Your financial situation is unfortunate but it has nothing to do with your rights against this lady. Whether you ask this lady to pay you and even sue her, you'll still have to find a new job.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relations