“Governor Walker is proposing to provide the University of Wisconsin System with the authority and flexibility that it has been seeking for years, while freezing tuition for two years to maintain college affordability for our state’s hard-working families,” she said. “These reforms will give the U.W. System the power to transform higher education in this state for the future by empowering leaders, protecting taxpayers and promoting long-term stability.”

But to his critics, Mr. Walker, in both his proposed cuts and in the discussion that arose over the Wisconsin Idea, is trying to capitalize on a view that is popular among many conservatives: that state universities have become elite bastions of liberal academics that do not prepare students for work and are a burden on taxpayers.

“This is a budget that serves Scott Walker for president, and it doesn’t serve Wisconsin,” said Jon Erpenbach, a Democratic state senator. “He’s trying to appeal to the most conservative of conservatives, the Republican voters in early-polling states. And there’s 5.5 million people back home saying, ‘Wait a minute.’ ”

Even some of Mr. Walker’s supporters, who cheered his initial run for the governorship and helped him survive a recall election in 2012, said they were questioning the governor’s budget proposal and its potential consequences for higher education.

“We are now facing a cut that will absolutely savage the infrastructure and quality of teaching and research to this university,” said John Sharpless, a Republican who is a history professor at the Madison campus. “What would be a shame for us in Wisconsin is if Scott leaves a wake of damage here on his way to the presidency.”

In an interview in her office here, Rebecca M. Blank, the chancellor of the Madison campus, said that if the governor’s budget was approved, she would have to raise out-of-state tuition and institute layoffs. She added that the proposed cuts were so large that if she eliminated five schools — nursing, law, business, pharmacy and veterinary medicine — she would still have to find other ways to trim costs.

“This is really big, in terms of its size on my education program,” Ms. Blank said.

Many residents in the liberal enclave of Madison, where Mr. Walker is deeply unpopular, see his willingness to slash funding for higher education as a reminder of his background: Mr. Walker abruptly dropped out of Marquette University, a Jesuit institution in Milwaukee, during the spring semester of his senior year.