More than 2 million Minnesotans would get a state income tax cut under a proposal that state House Republicans are pushing to hurriedly conform the state’s tax system to the new federal tax law, while about 179,000 filers would see their taxes go up.

Tax savings could range from $6 for those earning $40,000 to $338 for those earning $270,000, according to Department of Revenue figures.

Republicans in the state House want to drop the state’s second-lowest income tax rate from 7.05 percent to 6.75 percent by tax year 2020. But, in its drive to simplify a tax code that was thrown into disarray by last year’s federal tax overhaul, the GOP proposal would kill some deductions at the state level that were eliminated at the federal level — such as union dues, business expenses that are not reimbursed by your employer, moving expenses for work and others.

“We must pass a bill,” Rep. Greg Davids, R-Preston, chairman of the House Taxes Committee, said Tuesday. The panel voted in favor of Davids’ tax bill on Tuesday, with support even from the committee’s more conservative members. The full House could vote on the measure by next week.

In recent decades, any move to raise state taxes has provoked universal opposition from Republicans in the Legislature.

But the need to respond to the new federal law has left GOP lawmakers needing to collaborate with DFL Gov. Mark Dayton in order to avoid even more widespread tax increases on Minnesotans. And the House GOP proposal would lower state income tax rates for the first time since 2000.

Even DFL lawmakers on the Taxes Committee found plenty to like, fueling optimism that the two parties can come to terms on taxes. “I’m very encouraged by the bill,” said Rep. Paul Marquart of Dilworth, the lead DFLer on the Taxes Committee. Still, Republicans must overcome objections from Dayton and DFLers over the proposal’s long-term fiscal impacts and how it affects the respective tax burdens of wealthy vs. less prosperous Minnesotans.

Both Marquart and Dayton’s revenue commissioner raised concerns that the proposal would benefit business owners the most. “We’ve got to go a lot farther in evening the score for working families and senior families,” Marquart said.

Senate Republicans, also in the majority in their chamber, have yet to produce their own tax bill. Time is growing short, with lawmakers required to adjourn their regular session by May 21.

The need to retool Minnesota’s tax code is driven by the linkage between the state and federal tax system. Minnesotans determine their state taxes based on federal taxable income. If lawmakers do nothing, the state Department of Revenue would have to administer the state’s tax system based on the old federal law — leaving a labyrinthine hassle for both tax collectors and taxpayers.

If the state simply adopts the new federal rules in their totality, Minnesotans would lose a bevy of deductions that were cut by the law — such as personal and dependent exemptions — resulting in a tax increase for an estimated 870,000 Minnesota households, by an average of $489, according to the state Department of Revenue.

Large families are at particular risk because of the loss of personal and dependent exemptions.

The House Republican plan would use $107 million of state surplus money, plus money saved by eliminating some deductions, to reduce the number of people paying higher taxes by keeping some key deductions in place and lowering income tax rates.

The plan’s inclusion of a corporate rate cut is at the center of the conflict between Dayton and the Republicans.

“Unfortunately, this bill, like the federal tax law passed last year, provides more for businesses than for working Minnesota families when it comes to the rate reduction,” said Department of Revenue Commissioner Cynthia Bauerly.

Dayton’s own tax plan, released in March, would raise taxes on business to give a small income tax cut to about 2 million Minnesotans. Republicans used Bauerly’s appearance at the Taxes Committee hearing on Tuesday to attack Dayton’s plan to keep in place a health care provider tax — which funds MinnesotaCare, the state’s health insurance program for the working poor — that is scheduled to expire at the end of 2019.

Leaving the health care provider tax in place would mean higher taxes for Minnesotans of all incomes, according a Department of Revenue study released last week.

Bauerly questioned what the GOP proposal would do to the state’s long-term finances, which has been a priority of Dayton’s since taking office. “The bill does not reflect the fiscal sustainability that Minnesota needs,” Bauerly said in her testimony.

Davids was undeterred by the Dayton administration’s critique. “I’m not looking at differences so much as I am at similarities,” he said.

Both proposals would change how Minnesotans determine their income, scrapping the linkage with the federal government so the state can set tax policy independent of the federal government.

In a signal of his willingness to compromise to get a deal, Davids removed a controversial provision that would have punished so-called sanctuary cities like Minneapolis and St. Paul that limit their cooperation with federal immigration authorities by stripping them of local government aid.

On the other hand, Davids’ choice of an official song for his tax bill — an annual ritual by the colorful Taxes Committee chairman — did not inspire confidence that the two polarized parties could come to agreement. He chose Brothers Osborne’s “It Ain’t My Fault,” a song-length evasion of responsibility.