A sweeping proposal to cut taxes for Maine families and businesses could upend one of the most widely accepted practices in the country: the property-tax exemption for nonprofit organizations.

A recent budget plan by Republican Gov. Paul LePage calling for an overhaul of individual, corporate and sales taxes also would make Maine the first state in the nation to require colleges, hospitals and other large charities to go on the property-tax rolls in their municipalities.

“It would be a stunning development,” said Daphne Kenyon, a fellow at the Lincoln Institute of Land Policy in Cambridge, Mass. “I think there would be all kinds of reaction, from litigation to nonprofits’ possibly moving.”

Every state has laws that exempt churches and federally designated nonprofit groups from property taxes, although which holdings qualify can vary from place to place. Nonprofits say the special status is needed because they provide vital programs that governments often don’t.

LePage’s administration argues that the groups rely on local services, and the practice unfairly drives up property taxes for others. Churches and government-owned entities would be exempt under LePage’s proposal, which must be approved by the state Legislature.

“The cost of those services is being borne by Maine homeowners,” said Jonathan LaBonte, the director of Maine’s Office of Policy and Management.

While past stand-alone proposals to tax nonprofits have stalled in the Legislature, LePage’s plan appears to be the first one embedded in a governor’s prospective budget and is bringing far more attention to the idea than in the past.

Still, the provision’s fate is uncertain, with headwinds forming in communities and in the politically divided legislature. The piece related to nonprofits is part of a proposed budget that contains popular tax cuts but that also represents a major restructuring of the tax code, and would likely face months of debate and scrutiny over which parts to keep and which to toss out.

The plan reflects a growing national debate over the nonprofit exemption, especially in the Northeast. The region relies heavily on property taxes to fund government and has a particularly high concentration of tax-exempt academic and medical institutions, according to the Lincoln Institute.

“ In 2012, when more than one-third of the land in Providence, R.I., was owned by nonprofit organizations, the mayor aggressively pursued and obtained an agreement for millions in additional voluntary payments. ”

More than 200 localities in the U.S. have negotiated so-called payments in lieu of taxes from nonprofits instead, according to a report by the Lincoln Institute. Between 75% and 80% of such agreements are in the Northeast, with the largest share in Massachusetts and Pennsylvania.

In 2012, when more than one-third of the land in Providence, R.I., was owned by nonprofit organizations, the mayor aggressively pursued and obtained an agreement for millions in additional voluntary payments from Brown University and other colleges and hospitals. A few cities have imposed fees for a particular service on specific nonprofits.

But the LePage proposal would rewrite state law to include charities and schools on the tax rolls. The plan would help put into motion a sprawling overhaul he set out in his prospective 2016-17 budget.

An expanded version of this report appears at WSJ.com.