The package emerged from talks between three Senate and three House negotiators on the 108th day of the Republican-dominated Legislature’s session, now the longest ever.

The plan would raise $423 million during the fiscal year that begins July 1 — more than enough to balance the budget. The gap arose after lawmakers slashed personal income taxes in 2012 and 2013 at Republican Gov. Sam Brownback’s urging as an economic stimulus.

Disagreements among Republicans have prevented lawmakers from passing a full budget for the next fiscal year and threatened to force the state to furlough thousands of workers next week. But lawmakers passed a bill to avert a partial government shutdown, Brownback signed it and the new law took effect Saturday night.

The latest plan would increase the state’s sales tax to 6.55 percent from 6.15 percent and boost the cigarette tax by 50 cents a pack to $1.29.

The measure also would raise $24 million during the next fiscal year by increasing taxes for business owners. More than 330,000 business owners and farmers don’t have to pay income taxes on their profits under a 2012 policy.

The Senate on Saturday voted 34-5 against a plan with the same three elements. But GOP leaders hoped to attract votes with a proposal to lower the sales tax on food to 4.95 percent in July 2016, another to force the state to study eliminating all sales tax exemptions by 2020 and a third aimed at forcing down city and county property tax levies, starting in 2018.

“Maybe this will help get us on the road home,” said Republican Sen. Les Donovan, of Wichita, his chamber’s lead tax negotiator.

The Senate expected to debate the plan later Sunday. Majority Leader Terry Bruce, a Nickerson Republican, said if it passes, the chamber will attempt to approve a proposed $15.5 billion budget for the next fiscal year.

The House’s lead tax negotiator, Rep. Marvin Kleeb, an Overland Park Republican, had doubts that the new tax plan could pass his chamber. The House wasn’t meeting Sunday, forcing lawmakers to convene Monday for a 109th day.

“This is way outside of my comfort zone,” Kleeb told Donovan.

The most contentious issues are how much to increase the sales tax and how much to backtrack on the 2012 policy eliminating income taxes on farmers’ and business owners’ profits. Brownback has threatened to veto any plan that increases taxes for them by more than $24 million during the next fiscal year.

Legislators approved a limited tax proposal Saturday, a bill that more than triples a tax on HMOs’ premiums to raise $48 million toward closing the budget shortfall. The votes were 28-11 in the Senate and 63-41 in the House, and the measure goes next to Brownback, who is expected to sign it.

Other proposals enjoy broad GOP support. One would create a short-term amnesty program for delinquent taxpayers and another would eliminate most of the state’s personal income tax deductions.

Senate GOP leaders Saturday contemplated separating those items and the proposed cigarette tax from other issues and passing them in a separate bill, but they dropped the idea.

Each extra day of the Legislature’s annual session is costing the state more than $40,000. Lawmakers traditionally schedule their sessions to last 90 days, and the previous record of 107 days was set in 2002 — another year lawmakers increased taxes to close a budget gap.

Furloughs had loomed because employees’ compensation lags several weeks behind their work, so their pay for the two-week period beginning Sunday won’t be distributed until early July. The anti-furlough law enacted Saturday allows workers to stay on the job for several weeks even though the state won’t have the authority to pay them until a budget for the next fiscal year is in place.