The statute of limitations on debts in Texas is 4 years. If the debt was incurred before June 2006 write them a letter and tell them they are violating the Fair Debt Collection Practices Act as the debt is time barred and uncollectable.
If it is not that old contact the original creditor and see if you can make a payment plan. It seems like you already tried that and unfortunately, they can refuse to accept it. Make sure you go as high up as you can for an answer. Saying you have to pay a minimum makes me think its a collector instead.
If the debt is with a junk debt buyer you can still settle it. In writing, offer them a lump sum in return for a complete settlement on the debt. I would start with 10% and see what the response is. Make sure you stipulate in your letter that this debt will be paid in full when settled. Send your letter, detailing your hardships, certified mail with return receipt.
Lastly, if you have few assets you might want to just let the debt go and see how far they are willing to go. If they sue offer to settle. Wage garnishments are illegal in Texas so they can't attached your paycheck. Odds are they will settle if they think they'll get nothing otherwise.