The 12 medical facilities in western North Dakota saw their combined debt rise by 46 percent over the course of the 2011 and 2012 fiscal years, according to Darrold Bertsch, the president of the state’s Rural Health Association.

Hospitals cannot simply refuse to treat people or raise their rates. Expenses at those 12 facilities increased by 15 percent, Mr. Bertsch added, and nine of them experienced operating losses. Costs are rising to hire and retain service staff members, as hospitals compete with fast food restaurants that pay wages of about $20 an hour.

“Plain and simple, those kinds of things are not sustainable,” he said.

Many of the new patients are transient men without health insurance or a permanent address in the area. In one of the biggest drivers of the hospital debt, patients give inaccurate contact information; when the time comes to collect payment, the patients cannot be found. McKenzie County Hospital has invested in new software that will help verify the information patients give on the spot.

Mr. Kelly has pushed for the state, which has a surplus of more than $1 billion, to allocate money intended for the oil region specifically to health care facilities in the area. He has also asked for the state to grant low-interest loans so hospitals can borrow money for facility improvements and for the governor to convene a task force to study health care issues in the oil patch.

Aides to Gov. Jack Dalrymple say he is taking steps to bolster medical training in the state, proposing to spend $68 million on a new medical school building at the University of North Dakota and $6 million to expand the nursing program at Lake Region State College. Mr. Dalrymple, a Republican, has also increased Medicaid financing for the state’s rural hospitals.