ATLANTA — In 14 states across the country, attorneys general have filed lawsuits challenging the constitutionality of the recent federal health care overhaul. But here in Georgia, the Democratic attorney general has rejected such lawsuits as “frivolous” and “a waste of taxpayer money.” Now that position has led to calls from Republican lawmakers for his impeachment.

Thirty-one Republicans in the state legislature signed a resolution Tuesday calling for the impeachment of the attorney general, Thurbert Baker. Mr. Baker is also a Democratic candidate in the race, expected to be closely fought, to succeed Gov. Sonny Perdue, a Republican, who is prevented by law from seeking a third term.

Mr. Perdue has said he would circumvent Mr. Baker by appointing a “special attorney general” — a pro bono lawyer or legal team to challenge the constitutionality of the health care act on Georgia’s behalf. The governor said he believed the act violated the Constitution by requiring many citizens to buy health insurance from private companies.

Health care overhaul is unpopular with many Georgians, and Republicans have pressured Democrats to stake clear positions. Mr. Baker has said a constitutional challenge would be expensive and unsuccessful.