AUGUSTA — Lawmakers returning to work this week will soon face the question of whether Gov. Paul LePage should be punished for pressuring a charter school operator to rescind a job offer for a political adversary, House Speaker Mark Eves.

Eves, D-Berwick, said many lawmakers want to hold the Republican governor accountable for his alleged abuse of power, and options to be considered include a formal rebuke or a new investigation. All parties acknowledge that impeachment is unlikely to garner support.

Many Republicans want Democrats to give it a rest, and some wonder if pressing the issue could derail a busy legislative agenda.

“If that’s how he wants to set the tone, then we may have a rocky start to the session,” Assistant House Republican Leader Ellie Espling said.

Eves accused the governor of blackmailing school operator Good Will-Hinckley, and he has sued the governor for violating his rights.

The governor’s critics say the administration crossed the line by threatening to cut state funding for hiring Eves to lead the institution that helps at-risk students. The governor acknowledged he wanted Good Will-Hinckley to rescind the job offer.

The matter could come to the floor as early as Wednesday when lawmakers reconvene, said House Majority Leader Jeff McCabe, D-Skowhegan.

But the attorney general’s conclusion that a criminal investigation was not warranted may have taken the wind out of the sails of those Democrats beating the drum for an impeachment.

“If the Democrats or others go down that road, it will almost certainly derail the possibility of any productive legislation moving in this session,” said Michael Cuzzi, a former Democratic strategist.

Lawmakers are facing other weighty issues.

At the top of the agenda is legislation to address an epidemic of overdose deaths tied to heroin, fentanyl and other opioids. One proposal backed by Senate leaders from both parties and House Democrats would spend equally on hiring more drug agents and increasing treatment.

Other bills include reauthorization of Land for Maine’s Future bonds that expired without action by the governor; a renewed effort to expand Medicaid under the Affordable Care Act; additional welfare reform; and efforts to lower energy costs and boost the economy.

The last session ended on an acrimonious note with critics accusing the governor of overstepping his authority and the governor losing a legal fight over dozens of late vetoes.

The turmoil continued over the summer and fall as the Government Oversight Committee investigated the flap between LePage and Eves. The committee endorsed a report that found that the acting education commissioner withheld a quarterly payment from the Good Will-Hinckley school.

Eves and McCabe insisted that constituents don’t want the governor to escape the controversy scot-free.

“Members are weighing through their options for holding the governor accountable, because what he did is way outside the line of what’s acceptable,” Eves said.

One of the proposals in the House would call for a special investigation into the governor’s actions.

McCabe said there have been other times in which the governor may have overstepped his authority: LePage was accused of forcing out Maine Community College System President John Fitzsimmons, pressuring the former president of the World Acadian Congress to resign, intimidating unemployment hearing officers and conducting a secret review of the Maine Human Rights Commission.

Senate President Mike Thibodeau, R-Winterport, said people are weary of the political fights and want lawmakers to work together to move forward instead of rehashing old debates.

“Anything that is not going to directly affect the people who elected us in a positive way, then we should leave that at the door,” he said.