As DFLers and Republicans dig in on their budget divide, Gov. Mark Dayton on Thursday proposed a novel approach: Bring in a professional mediator who could help the two sides find common ground.

"We've got 28 days now and the clock is ticking and I'm willing to do everything and anything that I can think of, or anyone else can think of, that will be constructive to get this resolved," Dayton said. He said he would even welcome two mediators -- one picked by each side.

Republicans lawmakers quickly dismissed the idea.

"It is our time to step up and to lead and to do the job that we were elected to do," said House Speaker Kurt Zellers.

It's been just 10 days since legislators ended their regular session without a signed budget agreement. After a five-month session, Dayton and the GOP majorities in the House and Senate failed to reach an accord. Dayton vetoed nearly every major budget bill and Republicans rejected his call for higher taxes on the wealthy to the very end.

Since then, the situation has devolved to the point where some lawmakers are treating a July government shutdown as a near-certainty. Without an approved budget, state government's spending authority expires July 1, leaving a $34 billion operation to an uncertain fate.

The hard feelings deepened further on Thursday when Dayton announced he was instructing his commissioners not to testify before a legislative budget commission Thursday afternoon. The GOP legislative leaders had requested Dayton's finance and revenue commissioners both appear for questioning.

Dayton called the hearing "contrived political theater" and said he would not allow Republicans to publicly berate his agency heads.

Senate Majority Leader Amy Koch, R-Buffalo, and Zellers, R-Maple Grove, fired off a letter to Dayton reminding him that state statute says commissioners "shall provide the commission with full and free access to information" about the state budget.

Koch and Zellers convened the hearing anyway, with Democratic and Republican lawmakers spending about 45 minutes rehashing their budget talking points. They also discussed the possibility of using the commission's subpoena power to force commissioners to appear.

"For me, personally, if they don't show up at the next meeting, I will make the motion. It's disrespectful," said Sen. Mike Parry, R-Waseca.

Dayton and legislative leaders are scheduled to meet Friday morning behind closed doors.

Koch said she believes in the power of face-to-face meetings, adding that daily sit-downs would be even better. Dayton did not share that optimism.

Asked Thursday if he thought Friday's meeting would be fruitful, he said simply: "No."

Unless the GOP budges from its anti-tax stance, a seemingly irritated Dayton predicted, "we will see a repetition of the political grandstanding."

Minnesota has endured budget gridlock before, but no outside mediator has ever stepped in to help mend fences. Arturo Perez, a fiscal analyst with the National Conference of State Legislatures, said neither he nor anyone else at the organization could recall a third-party mediator settling any states' budget negotiations.

Unusual moves not ... unusual

But governors have made unusual moves in the past to find budget compromise.

In June 2005, then-Gov. Tim Pawlenty suggested he and legislative leaders head to Camp Ripley, two hours away from the lobbyists, media and staffers at the state Capitol, to work out their problems. "I've asked them to ... be prepared to stay there indefinitely until the negotiations are completed," the Republican governor said.

Democratic Senate leaders did not cotton to the road trip. That year, without a complete budget deal, state government shut down for about two weeks before a solution was found.

Former Gov. Jesse Ventura, of the Independence Party, employed his own special negotiating tactic. Frustrated with the lack of budget accord, the former professional wrestler once proposed locking his flatulent bulldog, Franklin, in a room with the Democratic Senate leader and the Republican House Speaker. He would let them out, he said, only when they had a deal. The threat was never realized -- they found a budget compromise without canine intervention.

Cooler heads may yet prevail in this year's impasse.

Despite Parry's threat to issue subpoenas, Zellers said he was not inclined to support such an extraordinary legal move.

Meanwhile, the state appears no closer to solving its gaping budget mess.

"There will a shutdown," predicted Senate Minority Leader Tom Bakk, DFL-Cook, a 16-year veteran of the Legislature. "It just seems unavoidable to me."

Rachel E. Stassen-Berger • Twitter: @rachelsb