One thing they're not considering: asking the wealthy to chip in. Instead, in a legislature that last week barred welfare recipients from using their benefits to go swimming or watch movies, the proposals that look most likely to succeed are sales and excise taxes that would be paid disproportionately by Kansas's poor and working class.
"You've got policymakers at this point who are unable to embrace the fact that there was a mistake made," said Annie McKay, the executive director of the left-leaning Kansas Center for Economic Growth. The think tank in Topeka argues that the state's deficit can't be eliminated without reversing some of the income tax cuts Brownback made in 2012.
Poor and working-class Kansans already carry a heavy burden under the state's tax system, compared to people of modest incomes in most other states. Among the fifth of the Kansas population with the lowest incomes, the average person pays 11.1 percent of what they make in state and local taxes, including sales taxes. Among the wealthiest one in every 100 Kansans, the average tax bill is just 3.6 percent of annual income, according to a recent report from the Institute on Taxation and Economic Policy.
People who make less are more vulnerable to increases in sales and excise taxes, since they spend more of their money buying basic goods and services they need to get by. This is especially the case in Kansas, where food is subject to sales tax. Kansans can receive a tax rebate for their food purchases, but those who make nothing or too little to owe income tax aren't eligible. They pay the sales tax on food in full.
The defense of the plan to raise sales and excise taxes -- the sales tax would increase from 6.15 percent to 6.3 percent, under one proposal -- is that people should be taxed on what they spend, not what they make, so as not to penalize them for earning more but instead to encourage them to save and invest their money.
"You're moving from taxing a productive activity to taxing a consumption activity," said Joseph Henchman of the nonpartisan Tax Foundation. "Most economists will say that it is good for economic growth."
In practice, though, people who don't have much money can't save or invest it. They have to spend it to get along. The more you make, the smaller the fraction of your income you have to spend to cover the basics. And wealthier households, which spend more on luxuries and entertainment, can always give up some of their purchases and keep the money in the bank if they don't want to pay the higher rate.
As a result, raising the sales tax equally for everyone means asking poorer households to pay significantly more, relative to what they earn.
The Institute on Taxation and Economic Policy's Meg Wiehe notes that in many states, average incomes have only increased among the richest groups in recent years. As a result, a system of taxation that depends more on the economic fortunes of the poor and the middle class might not produce increasing revenue in the future to meet the needs of growing states, unless the broad national trends change and incomes begin improving throughout the economy.
"Kansas has really shifted the responsibility for paying for taxes from those at the top with the most income, where income is growing, to those at the very bottom of the income spectrum, where incomes are stagnant or even declining," Wiehe said.
Poorer residents are required to pay a larger share of their incomes than wealthier residents in state and local taxes across the country. That difference is even greater among some states that don't have an income tax, such as Washington. There, the poorest fifth pay 16.8 percent of income in taxes on average, compared to just 2.4 percent among the very wealthiest, according to the report from the institute.
Brownback also has indicated he's willing to slow -- but not stop -- the implementation of his proposed tax cuts for the wealthy. However, he still seeks to eliminate the income tax over time. And some Republicans in the state legislature say they are fiercely committed to the original tax cuts and might oppose attempts to slow their implementation.
Lori McMillan, a law professor at Washburn University in Topeka who has talked about tax policy with several state legislators, said she thought they had good intentions. "They're not trying to break the backs of the poor," she said. "They're nice people."
Yet McMillan, who describes herself as conservative politically, worries that policymakers have failed to reckon with the consequences of their reforms for taxpayers and for the state's budget over the long term.
Even the proposed increases in sales and excise taxes would make up only a fraction of the deficit. To balance the budget for this year, Brownback and other policymakers have proposed temporary measures, such as transferring money out of the state's highway fund.