TOPEKA, Kan. — With the state facing a $400 million budget hole for the coming fiscal year, the conservatives who dominate the Legislature here say they are agonizing over the likelihood of doing something that did not seem to be in their DNA: raising taxes.

Just three years ago, many of these lawmakers passed the largest tax cuts in state history, saying they would lead to economic growth. But that growth did not appear, and after repeatedly trimming spending to close shortfalls, legislators again find themselves in a prolonged budget battle with no easy answers, where both houses of the Republican-controlled Legislature are proposing tax increases.

The reason: even anti-tax Republicans are acknowledging that there is not much more to cut without significantly hurting popular programs, including education.

The fault lines now seem to run along the question of which taxes to raise. Some believe that income taxes are off limits and that they should raise sales taxes to shoulder the entire burden. Others advocate a mixed approach and said income taxes should be on the table. Democrats argue that increasing sales taxes would be another blow to low-income Kansans to the benefit of the business class.