But Richard Carlson, the legislative liaison for the Revenue Department, presented a plan to lawmakers on Friday that would implement a much smaller income tax cut next year and hold those rates steady until the state hits a revenue growth target.

Under Mr. Brownback’s income tax cut, rates dropped this year to 4.6 percent on the top end and 2.7 percent on the low end. The lower rate was set to drop to 2.4 percent next year, but under the new budget proposal, it would fall only to 2.66 percent, while the higher rate would remain at 4.6 percent as scheduled. By 2018, the higher rate was supposed to dip to 3.9 percent, and the lower to 2.3 percent. But under the governor’s new proposal, the rates would remain at 2.66 percent and 4.6 percent.

The governor’s plan includes a mechanism for continuing the income tax decreases if revenue rises.

If revenue grows to 103 percent of the previous year’s amount, the plan calls for placing the additional revenue into a fund that the Legislature could use to implement more income tax reductions. Mr. Brownback’s plan also creates a budget stabilization fund that would use revenue growth to fill deficits.

He also has asked lawmakers to begin reducing the itemized deductions this year — those reductions were supposed to start in 2017 — and to increase sales taxes on liquor and tobacco products. Those changes, along with a tax amnesty for delinquents, would increase revenue by more than $423 million over the next two fiscal years, according to the governor’s estimates.

Representative Pete DeGraaf, a Republican, said that while he was pleased with the overall direction set by Mr. Brownback, he had concerns about elements of the governor’s plan.

“The path to zero is getting put into a reserve fund and then, unfortunately, rather than being automatic, it’s going to require future legislative approval,” he said. “My experience is if it doesn’t happen automatically, it doesn’t happen at all.”

Some Democrats said they had chuckled when they heard the governor’s income tax proposal because it sounded similar to that of former Representative Paul Davis, the Democrat who ran against Mr. Brownback last year.