Massachusetts lawmakers desperate for additional revenue are eyeing the endowments of deep-pocketed private colleges to bolster the state's coffers by more than $1 billion a year, asserting that the schools' rising fortunes undercut their nonprofit status.

Legislators have asked state finance officials to study a plan that would impose a 2.5 percent annual assessment on colleges with endowments over $1 billion, an amount now exceeded by nine Massachusetts institutions. The proposal, which higher education specialists believe is the first of its kind across the country, drew surprising support at a debate on the State House budget last week and is attracting attention in higher education circles nationally.

The idea has prompted a range of questions, including whether it is legal to infringe upon private colleges' tax-exempt status or single them out based on their wealth. It also faces significant opposition from the colleges and some skeptical lawmakers.

But proponents say the colleges' vast accumulations of wealth - Harvard University has the biggest endowment at $34 billion - and their often modest contributions to their host communities justify the assessment.

"When is a nonprofit not a nonprofit because of the wealth they are acquiring?" said Representative Paul Kujawski, a Democrat from Webster and chief backer of the legislation.

"It's mind boggling that one entity not paying taxes has $34 billion. How do you justify that?" said Kujawski, who serves on the influential House Ways and Means Committee. "When people can't afford to live. How do you justify not taxing them?"

University leaders criticized the plan as a gimmick that would backfire by hurting institutions that are pivotal to the state.

"You'd be taxing success here," said Kevin Casey, Harvard's associate vice president for government, community, and public affairs. "Over time, this would put us at a real competitive disadvantage, which would drastically hurt the Commonwealth."

Casey said it was understandable that lawmakers would search for new sources of revenue when economic times are tough. But he said the law would hurt colleges' fund-raising and financial aid initiatives.

The plan was introduced amid a national debate over whether elite colleges are hoarding their endowments. Members of Congress, including Senator Charles Grassley, Republican of Iowa, have questioned why elite universities do not spend more of their vast reserves to defray the cost of tuition.

Amid the scrutiny, some top-tier colleges have sharply expanded financial aid offerings, often replacing student loans with grants and waiving tuition for a greater number of families. At some of those schools, increases in financial aid are outpacing tuition increases.

The Massachusetts plan has also brought to the fore a more radical notion: whether certain colleges have amassed so much wealth that they no longer deserve to be tax-exempt.