Mr. Walker came to national prominence in 2011 largely because of his first statewide budget proposal, which relied on cuts to collective bargaining rights and increased health and pension costs for most public workers to help solve an expected budget gap. His latest proposal, which contemplates spending about $68 billion over two years starting this summer, quickly drew its share of critics, especially among those with ties to the state’s university system. But the address seemed muted compared with four years ago, when demonstrators could be heard screaming and pounding drums outside the legislative chamber as Mr. Walker spoke.

Mr. Walker’s proposal calls for cutting about $300 million, or 13 percent, in state funds from the University of Wisconsin System, which includes 13 four-year universities and enrolls some 180,000 students. Mr. Walker’s plan would also take the unusual step of removing the university system from direct state control to a “quasi-governmental” authority that could act autonomously on issues of personnel, procurement, capital projects and tuition.

As word spread in recent days that proposed cuts were coming, some in the university system expressed deep concern, likening the focus on the universities to Mr. Walker’s earlier clashes with public-sector labor unions. At the University of Wisconsin-Madison, the Faculty Senate this week condemned the proposal. Students said they intended to organize opposition.

Mr. Walker’s proposal needs approval from the State Legislature, which is controlled in both chambers by his fellow Republicans. Some of them voiced uncertainty about Mr. Walker’s suggestion that repairs for the state’s roads be paid for, in part, by borrowing $1.3 billion over the coming years. Mr. Walker rejected suggestions that he instead call for a higher gas tax. His office said the level of new bonding would actually be the lowest for the state in a decade.

Mr. Walker, who has often cited his record of lowering income taxes during his first four years in office, proposed no significant tax increases, and said the state’s funding should allow a typical homeowner to pay less in property taxes two years from now.