In Minnesota, the state estimates that residents could pay more than $400 million in additional state taxes in the next fiscal year because of the new federal law. That has set off a fight over how to respond. The state’s Democratic governor wants to give most of that money back to Minnesotans through tax cuts aimed at low- and moderate-income families; the Republican-controlled legislature wants broader-based tax cuts. Both sides say they must resolve the issue before the legislative session ends May 21.

Apart from the nine states with no broad-based income tax, nearly every state will face a similar decision. Almost all of the states base their tax codes in some way on federal definitions of income, before applying their own adjustments and deductions and setting their own tax rates.

The federal tax overhaul, which eliminated or capped several deductions and exemptions, effectively broadened what counts as income for some families. Previously, for example, a married couple with three children earning $70,000 might have been taxed on only about $36,000 of that income, according to the Tax Policy Center, a research group. The tax law, however, eliminated the so-called personal exemption and made other changes, which could increase this family’s taxable income to about $46,000.

At the federal level, those changes were more than offset for most families by lower tax rates and an increased child tax credit. In the example of a married couple with three children, the family’s federal tax bill would be lowered by more than $2,000 under the law. At the state level, however, the changes leave families owing tax on a larger share of their income, without the reduced rates or new credits to soften the blow.