Most of Mr. Brownback’s solution to fill the current hole comes through transferring more than $200 million from various state funds, such as one for highway projects and another for early-childhood education programs, into the state general fund. He also ordered a 4 percent budget cut to many, though not all, state agencies. He spared things like classroom funding and Medicaid, which would have sparked a lot of controversy if they were cut.

The fund transfers will require legislative approval, as will the cuts to agencies that are not part of the governor’s cabinet. The Senate president, Susan Wagle, faulted the governor’s approach, saying in a statement that he had “put the Legislature in a difficult position” and that she would have preferred to see spending cuts spread evenly throughout state agencies.

“That would certainly be a more fair approach than picking winners or losers and asking the Legislature to fill the gap,” she said.

One of the most controversial elements of Mr. Brownback’s plan is a cut of nearly 3 percent, or $40.7 million, to the state’s contribution to its pension fund. Even with the rollback, the state will still be contributing a greater percentage to its pension fund than before Mr. Brownback took office, Mr. Sullivan said. The administration sees it as a short-term solution but expected the Legislature to work out a more sustainable fix to a pension system that has an unfunded liability of about $10 billion. Proposed solutions have included issuing bonds to cover the unfunded liability or reamortizing the pension debt.

Jeff King, the Senate vice president, said he would have liked to see some of those sustainable solutions in the governor’s proposal rather than a slash in state contributions.

“The governor believes, obviously, that that is the way to go; I respectfully disagree,” Mr. King said. “I think meeting the obligation of our unfunded liability payments is vital.”

A state advocacy organization for children said that the governor’s proposal to transfer $14.5 million out of an endowment for early-childhood education programs could affect services in the future. The money comes from a settlement with tobacco companies and is used to fund things like Early Head Start, preschool and a program that trains parents to teach their young children skills at home.