ATLANTA — Georgia Republicans who want to eliminate the state income tax vowed on Wednesday that they would not pay for it by taxing groceries and housing.

Sen. Blake Tillery, R-Vidalia, secured agreement from a largely Republican study committee to neither impose a state tax on property or on grocery sales nor to increase the gasoline tax.

Tillery chairs both the Senate Appropriations Committee and a Senate committee that is studying how to abolish Georgia’s 5.19% income tax.

The move by Tillery, a candidate for lieutenant governor, illustrates the challenge. To eliminate the state income tax, lawmakers must either cut the budget or secure other sources of funding to maintain government services.

At the hearing Wednesday, senators heard from current and former officials from other sta

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