State Rep. Mark Hatfield, of Waycross, filed the legislation today.
The resolution says that Baker is required by the Georgia constitution to follow Gov. Sonny Perdue's direction and file a lawsuit challenging the Democratic-backed health care bill.
Baker has said the state lacks a viable legal claim to file a suit. Perdue has said he would bypass Baker and hire appoint an outside counsel as a special attorney general to bring a suit.
The Republican-led House would have to approve the resolution by a simple majority.
Baker is a Democratic candidate for governor.