ST. PAUL — Senate Republicans said Thursday they’ll propose cutting Minnesota’s lowest income tax rate as part of a $900 million tax relief package, an opening bid that will clash with Gov. Mark Dayton’s vision for a slimmed-down tax bill.

Top Senate GOP lawmakers wouldn’t specify how far their bill will cut the state’s first-tier tax rate below its current 5.35 percent level. Whatever the cut, most Minnesota residents would benefit — even higher earners would pay the lower rate on their first roughly $18,000 of income.

Combined with the GOP’s hopes of phasing out the state tax on Social Security income and creating a new college tuition tax credit, it’s a sign that Republicans will press Dayton to put more of a projected $1.65 billion budget surplus toward tax relief than the $300 million bill he laid out earlier this year. Sen. Roger Chamberlain, the Senate’s Tax Committee chairman, said a big tax break is overdue after the government has piled up years of consecutive budget surpluses.

“There are gobs of money pouring into the state coffers,” Chamberlain said. “It is time to give the money and some relief back to the workers in the state.”

The Legislature’s attention is quickly turning to setting a two-year budget. With Republicans now controlling the entire Legislature and a three-year gap since the last tax bill was passed, tax relief will play a prominent role in that debate.

Dayton devoted $300 million to a tax bill that prioritizes child care tax credits and increasing a tax credit for low-income residents. The Democratic governor was expected to release a revised budget proposal Friday, while House Republicans were aiming to unveil their own tax and budget bills next week.

In a letter to legislative leaders earlier this week, the governor warned against making drastic cuts to existing government programs to pay for a hefty tax bill. Senate Majority Leader Paul Gazelka signaled their budget would make some cuts but held off on providing details until today.

The marquee item in the Senate GOP’s tax proposal was their plan to reduce the state’s lowest of four income tax tiers — the first rate reduction in nearly two decades. Because residents pay graduated rates as their income grows, roughly 80 percent of Minnesota taxpayers would get a break — only the lowest earners whose tax payments are offset by tax credits wouldn’t see a cut.

Democratic senators quickly criticized the proposal as benefiting Minnesota’s millionaires. And Sen. Ann Rest, DFL-New Hope, said their proposal to phase out Social Security income would “become very costly.”

“I hope the Republicans’ plan will be cognizant of this risk and not jeopardize the long-term stability of our state’s fiscal outlook in an attempt to score political points,” Rest said.