I'm not a citizen of Kansas, but I live close enough to hear the news straight from the source in Topeka. From today's Kansas City Star.

TOPEKA — Kansas Gov. Kathleen Sebelius and legislative leaders said this afternoon that a special session on education funding will begin June 22.

Earlier today, the governor said that lawmakers must explore all options of finding money to solve the state’s education funding crisis.

That means expanded state gambling, tax increases and budget cuts are all options as lawmakers look for ways to answer a state Supreme Court order for $143 million more in school funding by July 1.

The court ruled Friday that a school funding package passed by legislators this year does not meet the requirements of the Kansas Constitution and ordered lawmakers to increase funding by another $143 million this year and, possibly, as much as $568 million next year.

Sebelius had called a meeting this afternoon with legislative leaders to discuss the session and the process for finding the money. She said she has some ideas, but won’t announce them until she has discussed them with lawmakers.

“I hope we enter this (process) as Kansans,” she said. “It’s clear that partisan plans don’t work.”

Backed by its Republican majority, the Legislature approved a $142 million increase in school funding in its session that ended last month. Legislators who supported the school plan quickly criticized the ruling and renewed calls for more controls on judges. Direct election of Supreme Court justices, term limits, reduced money for the judiciary and Senate confirmation hearings have all been proposed.

Sebelius, a Democrat, said lawmakers who say the court doesn’t have the authority to order the increase should brush up on their civics lessons.

“They need to go back and read the Constitution,” she said.

[emphasis added]

There's a link on that page to the text of the Court opinion.

I can guess you expect a uniformity of state constitutions that isn't there. If you have read the Kansas constitution, please enlighten us as to precisely how the state supreme court overstepped it.