ST. PAUL, Minn. » The shutdown of the state of Minnesota has forced the opening of a new hearing room here, where pleas have flowed forth, one after the next, for a week.

May locals dredge so barges can get through here along the Mississippi River even though laid-off state officials are not around to watch? Might 41 State Patrol officers not quite done with field training be deemed essential and sent back to work like others in the patrol?

Could state workers sign the adoption forms for a Minnesota couple who had been sitting in a Texas motel room with their new baby for the past week, unable to cross state lines without the paperwork? ("So our petition would be, um, could we please come home?" the woman asked the court Friday in the latest such hearing, conducted, in her case, by speakerphone.)

If the outlines of a government shutdown are simple — politicians cannot agree on how to spend money, so everything stops — the details are not. Since Minnesota officially closed its doors on July 1, the deadline by which the state’s political leaders were required to settle on a budget for the fiscal year, officials here have found themselves wandering a new labyrinth.

With the broadest shutdown in state history entering its second full week and no sign of a compromise on the horizon, political leaders in Washington, facing their own standoff and looming deadline, may want to ponder Minnesota — one cautionary reminder, if on a smaller scale, from the nation’s middle.

In many ways, of course, the situations are distinct, but Minnesota’s essential impasse sounds familiar: Republican lawmakers who control St. Paul want to rein in state spending and have rejected calls from Mark Dayton, the Democratic governor, to raise income taxes on the wealthiest Minnesotans.

Leaders in Washington disagree on what passing an August deadline without raising the debt ceiling would really mean (it has never happened), but some experts say it could result, along with devastation to the nation’s ability to borrow and to the broader economy, in a confusing, partial halt to some programs as the government has to pick and choose what it has enough cash to cover.

In Minnesota, carrying out a shutdown — and a relatively ordinary one, as these things go — has turned out to be a whole new, time-consuming government function, including convening the special hearings to weigh exceptions to the shutdown rules. The costs of closing (who knew it cost money to halt spending?) are themselves swiftly rising. And, puzzlingly enough, the shock of a shuttered Capitol, of 22,000 laid-off state workers and of barricaded state parks in the heart of Minnesota’s camping season seems, so far, not to have introduced urgency to the political negotiation.

No one knows exactly what the shutdown is costing Minnesota. For one thing, a final tally will depend on how long it lasts; for another, some of the people who might be estimating revenue losses and costs in various state departments right now are laid off.

"There’s nobody there to answer the phone call," said John Pollard, a spokesman for Minnesota Management and Budget.

But whatever the precise numbers, the topsy-turvy nature of freezing non-essential services in a state means that, too, costs money. Minnesota, for instance, had to pay the postage for sending out layoff warnings to 36,000 people as the new budget deadline grew close. Soon the state will need to pay unemployment benefits for the 22,000 workers who were ultimately sent home.

And the state is losing revenue it would otherwise be collecting, including $1.25 million a day in lottery sales (the lottery is closed), an unknown amount in parking and licensing fees the departments of health, education and administration are not getting, and about $52 million a month that the Revenue Department would ordinarily be bringing in if its compliance officers (now laid off) were scrutinizing tax payments.

And by the end of last week, there were other hints of financial repercussions for the state. Fitch Ratings lowered the state’s bond rating, noting the budget impasse, meaning that it will be more expensive for the state to borrow money.

Plenty of people here did not think things would actually come to this. The threat of a shutdown (exaggerated, in the eyes of some, until it happened) would be enough to force some last-instant compromise, as it usually does.

But that did not happen. Nor did an actual shutdown, and the immediate frustration of residents, state workers and others, seem to create any new rush to make a deal.

In a week of shutdown, Republicans and the Democratic governor appear to have gotten almost nowhere. In the middle of the week, Dayton announced two offers: one that would temporarily increase income taxes on Minnesotans making more than $1 million a year, and another that seemed to cede his income tax idea and instead to accept an increase in the cigarette tax as a way to raise revenues.

Republicans rejected both, saying that there were simply "not the votes" in the Legislature for any sort of tax increase. No talks have been held since, and recommendations from a group of Minnesotan elder statesmen, organized by Walter Mondale, the former Democratic vice president, and Arne Carlson, a former Republican governor, went nowhere either.

In fact, rather than seeming closer to resolution, the dispute has grown only more polarized, and outside groups are stepping in. The Alliance for a Better Minnesota has begun running radio ads blaming Republicans for the shutdown. The Minnesota Majority has bought billboards reminding motorists that the state’s rest stops closed when the state did. "Next rest area 138 miles, exit 214 — Iowa," one billboard reads, "Thanks a lot Governor Dayton."

Some of the smaller problems appear to be getting sorted out. The couple adopting a baby, for instance, was assured of a quick solution; though a package delivery service had said it was unable to deliver the needed adoption paperwork to the closed Capitol, top state officials said Friday afternoon that they would work around that, offering to drive to the delivery company themselves, if need be, to find the package.

But broader issues seem barely to move.

"That Minnesota would have a protracted government shutdown — I never thought that was possible," said Lawrence Jacobs, a political scientist here. "The big lesson from Minnesota is that the unthinkable is possible. You have a tendency to think in these sorts of situations it’s just a game of chicken, that there will be a resolution, that the debt ceiling will be lifted. But sometimes a game of chicken ends in a car crash."

© 2011 The New York Times Company