I did not mean to mark myself as "exempt" from having fed/state taxes withdrawn by an old employer. Is there anything I can do to avoid paying what I owe at this point?

Unfortunately not. But if you are unable to pay the tax you owe, all at once, you may make arrangements to pay the tax in installments.  The following FAQ tells you how to set up a payment plan. https://ttlc.intuit.com/replies/4678634