Topeka Gov. Bill Graves suggested he has little confidence lawmakers can send him an acceptable state budget in the remaining scheduled days of the Legislature.
The governor told reporters Thursday "there is a pretty good chance" he will have to call legislators back to the Statehouse in June to finish their work.
The last time legislators were called into special session by a governor was in 1989.
The state must eliminate a projected $700 million shortfall for the fiscal year beginning July 1. Legislators are taking their annual spring break and plan to reconvene May 1 to wrap-up business.
When lawmakers began their break, the House passed its version of the budget that was $106 million short on revenue; the Senate version was $306 million out of balance.
The Legislature must send the governor a balanced budget approved by both chambers by July 1. Otherwise state government faces the prospect of not operating after that date.
Legislators aren't scheduled to adjourn for the year until May 31, but typically their staff needs 10 days to prepare bills for the governor's desk, and the constitution gives Graves another 10 days to sign or veto measures.
That would mean legislators would have to finish work on the budget and most likely, a package of tax increases to fund it by May 11.
Graves said he doesn't think many legislators are ready to approve a budget and tax increases necessary to fund it.
"I'm not sure anyone has any guts to do anything," Graves said. "There's just a lot of posturing going on."
He added: "I think the special session there is a pretty good chance there will be one."
Republican legislative leaders have set May 11 as their target for wrapping up work, though aides have said lawmakers could go a few days longer without much problem.
If legislators kept working past mid-May, they would lose their chance to consider some or all gubernatorial vetoes.
Graves said he is concerned enough that lawmakers won't be able to finish their work on time that he has discussed the possibility with his staff and even a possible date for a special session.
Each day of a special session would cost taxpayers a minimum of $50,000, state officials say.
He said he would start one perhaps June 28, only a few days before the start of the next fiscal year, to force legislators to finish quickly.
"If they don't get their work done within the time frame they have established, I'm not going to necessarily feel any obligation to rush to bring them back," he said.