Topeka ? Lawmakers late Thursday failed to break an impasse on school funding but will try again today.

The Kansas Senate rejected a $128.7 million tax increase for schools, but sent the bill — put together by a bipartisan House group of Democrats and moderate Republicans — back to a conference committee for further work.

Some supporters of the tax increase said the vote was a setup because a majority in the Senate had consistently opposed tax increases.

“I’m growing tired of these games of chicken,” said Sen. David Adkins, R-Leawood.

Gov. Kathleen Sebelius, who visited with senators in the moments leading up to the debate, urged cooler heads to prevail.

“It’s either close or it’s done (for the session),” Sebelius said. “I do think they’re reaching a point where a serious effort has to be made.”

Sen. Mark Buhler, R-Lawrence, who has supported tax increases for schools, voiced along with many other lawmakers, frustration that the two chambers remained far apart on the session’s 87th day, including nine days of the wrap-up session.

“If the horse dies, dismount,” Buhler said.

The House coalition called its $128 million plan a compromise from its earlier approved $155 million proposal. The Senate has approved measures that would provide increased funds for schools by dipping into cash reserves and delaying pension system payments.

“We are trying to offer an olive branch to the Senate,” said Rep. Paul Davis, D-Lawrence. “We are willing to negotiate with them in good faith.”

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Some lawmakers talked about calling an end to the session without an increase for schools, but others were adamant to keep working.

“We cannot adjourn without doing something for schools,” said Rep. Rob Boyer, R-Olathe.

The Boyer-Davis plan would have the increased the state income tax 3.75 percent and the state sales tax from 5.3 cents per dollar to 5.46 cents per dollar.

Funding would have gone to increase base state aid, programs for students at risk of failing, students learning English, and special education.

The plan would have increased state funding to the Lawrence school district by about $2.4 million.

More negotiations are expected today.

Senate President Dave Kerr, R-Hutchinson, said the Legislature was resolving final bills to focus on school finance.

“It’s now time to vote seriously on school finance and go home,” he said.

Sebelius said the Legislature needed to produce a finance plan.

“The big job left to be done, which was the big job in January and February and March and April and now we’re in May, is to adequately fund schools,” she said.

The Associated Press contributed to this report.