BISMARCK, N.D. — Since Californians shrank their property taxes more than three decades ago by passing Proposition 13, people around the nation have echoed their dismay over such levies, putting forth plans to even them, simplify them, cap them, slash them. In an election here on Tuesday, residents of North Dakota will consider a measure that reaches far beyond any of that — one that abolishes the property tax entirely.

“I would like to be able to know that my home, no matter what happens to my income or my life, is not going to be taken away from me because I can’t pay a tax,” said Susan Beehler, one in a group of North Dakotans who have pressed for an amendment to the state’s Constitution to end the property tax. They argue that the tax is unpredictable, inconsistent, counter to the concept of property ownership and needless in a state that, thanks in part to wildly successful oil drilling, finds itself in the rare circumstance of carrying budget reserves.

“When,” Ms. Beehler asked, “did we come to believe that government should get rich and we should get poor?”

An unusual coalition of forces, including the North Dakota Chamber of Commerce and the state’s largest public employees’ unions, vehemently oppose the idea, arguing that such a ban would upend this quiet capital. Some big unanswered questions, the opponents say, include precisely how lawmakers would make up some $812 million in annual property tax revenue; what effect the change would have on hundreds of other state laws and regulations that allude to the more than century-old property tax; and what decisions would be left for North Dakota’s cities, counties and other governing boards if, say, they wanted to build a new school, hire more police, open a new park.