SALEM, Ore. — The allegations swirling around Gov. John Kitzhaber and his live-in fiancée did not seem to bother Oregonians much when they re-elected him last fall to an unprecedented fourth term. But now, with hints of scandal tumbling out almost by the day — about the business dealings of the fiancée, her previous marriage and her role in state government — the reaction has descended into a mix of tittering gossip, outrage and dismay, threatening to tarnish the last years of one of the state’s most enduring politicians.

Mr. Kitzhaber, a 67-year-old Democrat in a heavily Democratic state, faces a long list of problems: two petition efforts to recall him, demands for his resignation from various newspapers, and an ethics investigation by the state into the business dealings of his fiancée, Cylvia Hayes. Separately, the Oregon attorney general, Ellen Rosenblum, said Monday that she was opening a criminal investigation of the couple.

The inquiries stem from contracting work that Ms. Hayes, 47, a clean-energy consultant, performed and was paid for while living with the governor and advising him on clean-energy issues. Those issues have long been a priority of Mr. Kitzhaber’s administration, but now they are bound up in, and perhaps undermined by, questions of whether love and politics got too cozy in the governor’s mansion.

But the deeper trouble is that after 12 years in office, the governor’s enemies and critics — and erstwhile supporters, who think he has simply stayed in office too long — have grown like compound interest over everything from his laid-back management style to the disastrous rollout of the state health insurance website, which never fully worked and cost hundreds of millions of dollars.