DFL Gov. Mark Dayton said Monday he was willing to drop his call for more taxes on millionaires, but warned that the state budget stalemate will continue unless GOP leaders agree to raise more revenue and spend more money.

In a letter to Republican leaders, he said he was willing to consider sales tax changes, increasing "sin" taxes or the elimination of tax breaks to get a deal done. But he drew a hard line against cutting spending as deeply as Republicans have urged.

"I'm just offering various possibilities. I want to get this resolved. The people of Minnesota want to get this resolved," Dayton said, standing in front of the closed-down State Capitol on Shutdown Day 11.

In response, Republican leaders said that Dayton is going down the wrong road.

"It's not about who we are taxing and how much, but: What do you want the money for?" said Senate Majority Leader Amy Koch, R-Buffalo.

The continuing standoff leaves the state watching as the politicians grow ever more settled in the intractable positions that have left many parts of government idle, waiting for a breakthrough to close the $5 billion state budget gap and get the state ticking again.

While the politicians are stuck, the courts have been deciding which programs get funded and which must be halted.

A court decided Monday that highway rest stops could not reopen during the shutdown but meals for homebound elderly should be funded. Meanwhile, the Minnesota Supreme Court set a hearing date for Republican lawmakers' argument that the courts should not be deciding funding at all.

Winners and losers

Highway rest stops are not a core function of state government, wrote Ramsey County Chief Judge Kathleen Gearin in a decision that upheld a finding by Kathleen Blatz, special master appointed to review funding requests during the shutdown.

"The failure to fund the continued operation of rest stops along Minnesota's highways is no doubt adversely impacting the ability of commercial truck drivers within Minnesota to adhere to their federally mandated rest requirements and will likely result in increased costs to drivers and trucking firms," Blatz wrote. But she said the rest stops' operation is not critical and therefore she could not recommend their funding.

Blatz and Gearin also agreed that the Nursing Board cannot be funded to accept applications for new nursing licenses, the state's Drivers and Vehicle Services department cannot keep the electronic vehicle registration system running for auto dealers, the state Health Department cannot review the city of Minnetonka Beach's water main plans and addiction recovery services should not be funded.

Store to Door, a nonprofit that provides meals to homebound elderly, had better luck. The court ruled that feeding the elderly is a "critical core function of government" and ordered funding for the State Nutritional Support grants and the State Nutritional Expansion Fund.

Four Republican senators and two House members have filed suit, saying it is unconstitutional for courts to make such spending decisions. The Minnesota Supreme Court on Monday scheduled July 27 oral arguments on their petition.

With no political breakthrough on the horizon, the shutdown could last that long or beyond. Asked Monday how long he would be willing to keep government shut down, Dayton replied: "My term expires on January 5th of two thousand. ... " He trailed off with a laugh.

"My focus is on getting this resolved as quickly as possible," he added. "I want to see Minnesota back working again."

Dayton said he awaits a counteroffer from Republicans in response to his revenue suggestions. He said he still would prefer that the GOP adopt his proposal to raise taxes for the wealthiest Minnesotans but would "conceivably" sign a measure that placed the burden elsewhere.

Republican leaders Monday did not appear ready to give Dayton a counterproposal anytime soon.

"We'll keep working on that," Koch said. Republicans have not put a concrete offer on the bargaining table since the start of the shutdown July 1.

Republicans leaders said they would rather pressure the governor to call a special session immediately to pass a so-called "lights on" bill, which would allow for restarting state spending. Dayton, like his Republican predecessor, Tim Pawlenty, and other governors before him, has repeatedly said that calling a special session without a budget deal in place is a non-starter.

"I'm going to hold out for a fair budget for the people of Minnesota. I wouldn't have started down this path if I weren't willing to do it," Dayton said, announcing a tour of the state to tout his budget position. He will travel to St. Cloud on Tuesday and Rochester, Winona, Albert Lea and Moorhead later in the week.

Shutdown win

Meanwhile, Pawlenty, who presided over the 2005 government shutdown, has worked to turn that struggle into a presidential campaign asset.

"I've got the record of toughness better than anybody else in this race. My goodness, I was the first governor in Minnesota's history to shut down the government," Pawlenty said on "Meet the Press" Sunday.

The former governor has also said he should have let that shutdown last longer and claimed he "won" that shutdown.

Some current lawmakers said it's tough for anyone to claim victory in such a tussle.

"I don't think anybody wins, honestly," said House Majority Leader Matt Dean, R-Dellwood. "Everybody gets a lot of mud on them and it's bad for everybody."

Staff Writer Mike Kaszuba contributed to this report. Rachel E. Stassen-Berger • Twitter: @rachelsb