The resolution from Republican state Rep. Mark Hatfield claims Thurbert Baker has "abdicated his authority and has committed an act against the state of Georgia." It has 30 co-sponsors, all Republican.
The resolution claims Baker - one of five Democrats running for governor - is required by the Georgia constitution to follow Republican Gov. Sonny Perdue's direction and challenge the Democratic-backed health care bill.
Perdue has said he will bypass Baker and appoint an outside counsel as a special attorney general to pursue a lawsuit pro bono on behalf of the state.
In an interview on Tuesday, Baker said he is "disappointed that the Legislature would respond this way."
He stood behind his decision not to sue, saying the state lacks a viable legal claim and a lawsuit is almost certain to fail.
"If the Legislature chooses this route, I look forward to have a very public legal debate about this issue," Baker said.
The resolution would need to be approved by a simple majority the GOP-led House. There would then be a trial in the state Senate led by the state's chief justice. A two-thirds vote would be needed to convict. That would require Democratic support in the chamber where Republicans hold 34-22 majority.
But the measure's future in the House didn't seem promising.
House Speaker David Ralston, who would need to get the measure for a vote on the floor, said he didn't support the proposal.
"Impeachment doesn't serve the people of Georgians," Ralston said.
Ralston backs a separate GOP resolution that would direct the attorney general to follow Perdue's direction to sue.
"I do wish the attorney general would remember that his client is the people of Georgia, not the Obama administration, but I don't think impeachment is the answer," he said.
A spokesman for Perdue repeated the governor's claim, made last week, that impeachment is a function of the legislative branch. He had no additional comment.
Hatfield said he supports a harsher sanction because Baker is guilty of "a very serious breach of trust with the people of Georgia."
"He is ignoring his constitutional duty to the office to which he was elected," Hatfield said.
Fourteen states have joined in a federal lawsuit challenging the sweeping federal health reform law backed by President Barack Obama.
Florida Attorney General Bill McCollum, a Republican, led the effort to file the suit that claims Congress doesn't have the constitutional right to force people to get health coverage. It also claims the federal government is violating the Constitution by forcing a mandate on the states without providing resources to pay for it.
McCollum is also running for governor of Florida, which prompted complaints from Democrats in his state that the suit was a political ploy.