Trouble may be too strong a word. But you have an obligation to report all income, from whatever source derived. That said, failing to report income from a government source is a pretty good way to get noticed. Your best course of action, if you have already filed and your tax return has been accepted, will be to file an amended tax return, using Form 1040X. Instructions are below.
If you have not yet filed, by all means include the income from Form 1099-G.
Failure to report income will bring a notice later in the year from the IRS, identifying the source and amount (they get a copy of all those forms that are sent to you) and assessing tax, interest, and penalties.