In Virginia, can I deduct the percentage of capital gains distributions that come from US government obligations?

Yes. Virginia law allows a subtraction for income (interest) derived from obligations or income (dividends and gains) derived from the sale or exchange of obligations of the United States, and on obligations or securities of any authority, commission or instrumentality of the United States to the extent the income is included in federal adjusted gross income. The amount to be subtracted is the income less any related expenses already deducted on the federal return. The subtraction applies only to income from direct obligations. For information on obligations that qualify for the subtraction, see PD 94-281.