You need to file the unemployment information with your 2010 income tax form, showing the unemployment as money you received. Because if you don't it will cross match, and very shortly, within the next year, you'll be hearing from the IRS, with penalties attached. The IRS does not know, and does not care that you have been assessed for the money back. This was done by the state system.
"They're going to make me pay it back" doesn't mean you will have to. It doesn't mean you have yet. If this overpayment was not the result of fraud, you may never be pursued to recoup the money. If you have merely received an unfavorable decision on a claim, and they have determined you overpaid, you may not be obligated to pay this back until you file for unemployment again, at which time it would be taken from your next claim. But that has nothing to do with what you received in 2010, or your 2010 income taxes.
They may never push this, and you may never have to pay it back. But one thing is for certain. You got it. This last year, you got it, and it is considered taxable income. What MAY happen, in terms of your paying the money back, probably isn't ever going to be deductible.
If you paid the money off in a lump sum during this year, you might possibly talk to a tax professional about filing an amended return...but you know, I'm by no means sure that would fly. Others will know more than I. But right now, pay the taxes on this income or you'll be in a world of trouble.