ST. PAUL — Leading Minnesota lawmakers sorted out a tax package Thursday that will require the wealthy, smokers and corporations to pay more, a cornerstone of the next state budget that they’re running short of time to pass.

The top 2 percent of income earners will see a portion of their earnings taxed at a rate 2 percentage points higher. The per-pack tax on cigarettes will rise by $1.60. Some corporate tax preferences will go away. Sales taxes will be imposed on business transactions involving warehousing, electronic equipment repair and commercial maintenance.

But there won’t be any increases to the alcohol tax, as House Democrats had sought. Nor will there be a temporary tax surcharge on incomes of $500,000 or more as a way to erase the state’s debt to schools that accumulated during prior budgets.

Gov. Mark Dayton, House Speaker Paul Thissen and Senate Majority Leader Tom Bakk said during a hastily arranged news conference Thursday that the agreement will pave the way for the Legislature to pass its budget before a mandatory Monday night adjournment to the session. And they said the tax increases — a combined $2 billion over the next two years — will plug a $627 million projected deficit and pay for a big jump in education spending and other priority programs.

“We are on the cusp of an important course correction in our state’s history,” Thissen said.

All three in the state’s all-Democratic power alignment made concessions that they said were needed to close the deal.

“This is the linchpin of the session,” Bakk said. “Now everything will fall in” place.

The new income tax mirrors a proposal Dayton laid out back in January: Couples will pay 9.85 percent on every taxable dollar they earn above $250,000, and singles on earnings above $150,000. The current top rate is 7.85 percent. The new tax is expected to generate slightly less than $1.2 billion.

Minnesota’s cigarette tax would jump to $2.83 per pack — shooting 30 cents past what Wisconsin charges and going well beyond what the rest of the neighboring states assess. It would bring in $370 million, but tens of millions of dollars would come through higher excise taxes on snuff and cigars, too.

But the top Democrats said there will be tax relief too. They said there will be $400 million put into local government aid and direct property tax assistance programs. In addition, cities and counties will save about $100 million per year through an exemption in the sales taxes they pay, which could ease pressure on homeowner and business property tax rates.

Republicans said Democrats were going too far in their push for higher taxes. Senate Minority Leader David Hann said the taxes targeted at businesses will trickle down the retail chain.

“This idea that it is only going to affect businesses is nonsense. It is ultimately going to affect consumers and everybody that buys anything those businesses support,” Hann said.

Despite total legislative control, some Democratic goals were in doubt thanks to House-Senate tension. They were stuck on a proposed minimum wage hike, with the House holding to a plan to boost it to $9.50 by 2015 and the Senate holding to a $7.75 wage.

By Thursday evening, the House and Senate had given final approval to a couple of budget bills.

One was a package of economic development programs that boosts state spending in that area by $90 million. It includes incentives for businesses to add to their payrolls or expand their physical presence in the state. The bill also contains $5 million in forgivable loans to a Fortune 500 pharmaceutical company considering a Minnesota outpost staffed by 200 high-wage employees. They also passed a public safety finance bill, which funds law enforcement activities and the courts. It includes pay raises for state judges.

But the bigger dominoes have yet to fall.

Rep. Paul Marquart, chairman of the House Education Finance Committee, said negotiators hoped to finish work on that package later Thursday. It’s a big chunk of the budget, registering $15.7 billion over the two years.

A key feature of that bill is an expansion of state assistance to school districts for full-time kindergarten programs. More than 75 percent of Minnesota kindergartners attend a full-day class, but 10,000 of them are in programs that require parents to pay a fee for the extra time, at an estimated cost of $26 million. The bill would push all of the costs to the state and enable districts that can’t afford to offer full-day kindergarten the opportunity to do so.

House Democrats entered session promising to fully repay IOUs to schools. The state had deferred some payments to patch a leaky budget. Now they will wait to see if a brightening economy will do it for them. Any money left over at the end of this fiscal year will go to make schools whole. Thissen said Democrats will address any remaining school debt next year.