Joining the ranks of Republican governors taking aim at the power of labor unions, the new chief executive of Illinois, Gov. Bruce Rauner, said on Wednesday that the state should ban some political contributions by public employee unions and allow local “right to work” laws.

In his first State of the State address, Mr. Rauner called for contracts that reward government employees’ performances rather than longevity, and for an overhaul of laws that he said inflated the cost of public projects by mandating how contractors pay workers.

The reaction from Democrats, who control the state legislature, was remarkably muted, not dismissing the governor’s ideas out of hand. But in a state where Democrats have large majorities in both houses and are the primary beneficiaries of union support, enacting any curb on labor’s power will be difficult.

“Government unions should not be allowed to influence the public officials they are lobbying, and sitting across the bargaining table from, through campaign donations and expenditures,” Mr. Rauner said. Noting that many companies that do business with the state are prohibited from making political contributions, he said the ban should also apply to groups like hospitals that receive state grants.