I assume you're referring to an overpayment of unemployment benefits, correct? If so, then you will have no choice but to pay it over time, and the state will have no choice but to accept that situation. Granted, they can take additional action such as placing a lien on your property and deducting the overpayment from future benefits, but the bot***** *****ne is that they can't squeeze water from a rock. If you can't pay them back in a lump sum, then they're stuck with you paying over time.
You should note, however, that you will have to pay interest and penalties in addition to the overpaid amount. Moreover, it's possible that they will seek to have you criminally prosecuted since it is a crime to falsify information in order to obtain higher benefits. However, just because they determined that it was a fault overpayment doesn't mean that you actually committed a crime or that they can prove that you committed a crime. It's one thing for them to determine that you purposely misrepresented to facts, and it's another thing to convince a judge and jury that you did so. Considering the overpayment is fairly small, I would not expect them to seek to prosecute (though it also depends on what exactly they claim you did).
Bot***** *****ne is that if I were you, I would contact them ASAP to make payment arrangements. Your good faith attempt to repay will certainly help in this situation.
Does that answer your question? Please let me know if you need clarification, as I am happy to continue helping you until you are satisfied.