Just wait and try not to worry - you will probably get back whatever federal refund was showing on your return, even without including the 1099-G.
Because of the latest change in tax law (see below), your "missing 1099-G" may not have any effect on your refund.
In normal years, the IRS won't start "matching" the tax forms reported on your return with their records until after tax filing season is over (much later in the year). At that time, they'd send you an automated notice asking about the missing form and proposing a higher tax bill because of the unreported income.
This year is different because the Congress just passed a bill exempting up to $10,200 of unemployment income from federal tax (for those making less than $150,000). It remains to be seen what procedures the IRS will put into place to deal with this late-breaking tax "gift".
