Does your 1099-G have federal income tax withheld in box 4 or state income tax withheld in box 11? That's how you get credit for the tax that was withheld. But you have to report the gross amount in box 1 as income. It's just like as a W-2 that shows your gross pay, before taxes, in box 1, and shows the tax that was withheld.
When you enter your 1099-G in TurboTax check the box that says "Federal or state income tax was withheld on this payment." Then on the next screen enter the tax amounts.