The measure's future in the House didn't seem promising.
The resolution from Republican state Rep. Mark Hatfield says Baker has "abdicated his authority and has committed an act against the state of Georgia." It has 30 co-sponsors, all Republican.
The resolution says 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 with The Associated Press 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 of 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 a 34-22 majority.
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 Georgia," he 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 statement, 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 Obama.