Gov. Mark Dayton wants hundreds of millions of dollars to bring preschool classes to every Minnesota public school, and stricter stewardship of the state's water quality.

Republicans who control the House want big new tax cuts, preferably with a "b" for billion in the total. DFLers who run the Senate are pushing a substantial transportation spending increase, to a level that could only be covered with some type of tax increase on drivers.

With one week left to the legislative session, the priorities of those in charge of state government have come into focus. It's a volatile mix peppered with dozens of other disputes large and small between the DFL and GOP. If Dayton and legislative leaders can bridge those differences and bring the session to an orderly end, voters will see a demonstration of what politicians in St. Paul constantly promise but much less frequently deliver: bipartisan cooperation.

"It's doable. But it's going to take a lot of cooperation on their part," Dayton said Sunday, referring to House Republicans. For the session to end on time, Dayton said, Republicans must accept they are dealing with a DFL governor and Senate majority, and only expect to get about a third of what they want.

Leading lawmakers, including House Speaker Kurt Daudt and Senate Majority Leader Tom Bakk, along with several top administration officials, were back at the Capitol Sunday afternoon for private budget talks. Republicans, too, say they are committed to compromise.

"We want to work together, be reasonable and not have people digging in their heels," said Rep. Kathy Lohmer, R-Stillwater, an assistant majority leader with a strongly conservative voting record.

But dig into the details of what's left to be decided, and you quickly find lines that Lohmer — and many other lawmakers — will find difficult to cross, even with the financial padding of a projected $2 billion budget surplus.

Start with the total amount of state spending for 2016-17. Dayton wants just shy of $43 billion, and Senate Democrats a bit less than that. House Republicans want a total budget of just under $40 billion, although they also want to reroute about $300 million from the state treasury into dedicated road and bridge repair funds, and to cut taxes by $2 billion.

The two-year state budget when Lohmer entered office in 2011 was about $35 billion. "At the time, we were all about, 'not a penny more,' and we were fighting for that," she said. "Now we're looking at $43 billion. How can that be sustainable?"

To keep spending on programs lower, House Republicans voted to eliminate the state property tax paid by businesses, phase out state taxes on Social Security income, and grant a one-time, $1,000 personal exemption for two years worth of state tax filing. To free up dollars for those tax cuts, they trim state spending in a number of areas, particularly in health and human services programs.

The most noticeable change would be the elimination of MinnesotaCare, a 20-year-old program that Republican leaders say is serving many recipients who, in every other U.S. state, are instead now getting coverage through state health insurance exchanges under the Affordable Care Act. Doing so would save the state about $1 billion over two years.

For Democrats, the program is fundamental to the mission of state government.

"People actually rely on MinnesotaCare, the most vulnerable people in our state: the elderly, disabled, children in need of protection, low-income families," said Sen. Tony Lourey, DFL-Kerrick. "These are the folks across Minnesota that look to us to make sure that they have a decent life."

One issue has brought agreement between the two parties: the need for a major new state spending to repair aging, battered roads and bridges. But where Republicans want to shift money from the general fund and leverage state debt capacity to bankroll driving-centered projects, Senate Democrats and Dayton favor raising new money for roads, bridges and transit in the form of a new gas tax at the wholesale level, and higher vehicle registration fees.

Increasingly, Republicans have come to see simply stopping a gas tax increase as a political win. "They've got a really tough uphill argument to make that we need a gas tax," Daudt said Sunday.

While Republicans see a chance to sink a politically unpopular proposal, the DFL-led Senate has voted twice in two years to raise a gas tax. Bakk said that if House Republicans expect to come out of the session with significant tax cuts, then it will have to be in exchange for some of the new transportation dollars sought by Senate Democrats.

"I'm willing to consider a tax bill for consideration of a transportation bill," Bakk said. He reminded that, given the projected surplus, that neither a tax bill nor a major transportation bill is necessary to keep state government operating the next two years, meaning the current session could end without either.

All of this: Dayton's education spending boost and water buffer proposal, the House GOP's tax cuts and MinnesotaCare plans, and the Senate DFL's transportation wishlist and goal of leaving several hundred million dollars in reserve funds, will all be in play this week as the governor, Bakk, Daudt and other players negotiate in pursuit of a deal in time to avoid a special session.

An overtime session would be particularly challenging this year with the ongoing Capitol renovation. Right now, contractors have plans to start clearing out the House and Senate chambers the day that session ends. Delaying that would mess with the project's timeline, and would likely add to a total price tag already north of $300 million.

Said Matt Massman, the commissioner of the Department of Administration: "They really need to finish on time."