ST. PAUL — Minnesota’s legislative session slid toward a breakdown Wednesday as the Republican-controlled Legislature prepared to send spending bills to Democratic Gov. Mark Dayton without a budget deal.

Five days before a mandatory adjournment deadline, both House and Senate took final votes on pieces of a budget that would slash projected spending levels by $5 billion.

Dayton has repeatedly vowed to reject spending bills without an overall budget agreement. He wants to raise $1.8 billion in new taxes, mainly by creating a new income tax bracket for the top 2 percent of earners. The first-term governor said Wednesday he is becoming more pessimistic that the session could expire without a new two-year budget in place, forcing a special session and potentially leading to a government shutdown.

“I don’t think there’s any indication of willingness on their part to negotiate at this stage,” Dayton told reporters Wednesday.

GOP leaders in their inaugural session accused Dayton of failing to engage in serious budget talks, even as they insisted that the session could still finish on time with his signature on a complete budget. They criticized his negotiating style, calling it “erratic.”

“There’s absolutely still time, but what we will need is some leadership. We’ll need some leadership from the guy in the corner office,” said Senate Majority Leader Amy Koch, moments after lamenting “the governor’s leadership or lack thereof.”

Dayton and the GOP-controlled Legislature are gridlocked over taxes and the level of spending. Dayton’s latest tax proposal was offered on Monday, nearly halving his previous plan to raise taxes. Republicans want to cap spending at $34 billion and refuse to entertain tax increases or other new revenue as they seek to shrink government.

“They want it all their way,” Dayton said.

The governor is expected to speak to rank-and-file GOP lawmakers in a joint caucus meeting on Thursday, at the invitation of legislative leaders.

Action on the budget bills was expected to continue into the evening Wednesday.

The Senate approved a state agency bill that would freeze employee pay and cut the state work force and approved deep cuts to projected health and social service spending, the fastest-growing part of the state budget. The House approved spending for environmental programs after an all-nighter that featured votes on a tax bill and spending bills for public schools and colleges.

Minnesota’s current budget runs through June. Without a new budget in place, parts of state government would shut down on July 1.

The Senate approved a tax bill that would phase out state aid to the same three cities. A Senate vote was also expected on a public schools spending package that would eliminate racial integration aid for Minneapolis, St. Paul and Duluth schools and a tax bill that would phase out state aid to the same three cities. Both bills passed the House earlier Wednesday.

Meanwhile, the final step in a push for a statewide vote on gay marriage could come in the House as early as Thursday.

The proposed constitutional amendment banning gay marriage cleared a final procedural hurdle Wednesday after passing the Senate last week. Dayton said Wednesday he would oppose the amendment “with every fiber of my being” but has no power to block it from going to voters.