ST. PAUL — A bitter budget standoff sent Minnesota spiraling Thursday toward a wide-ranging government shutdown, threatening to shutter state parks on the brink of the Fourth of July weekend and lay off tens of thousands of workers if a deal isn’t struck by midnight between the state’s Democratic governor and GOP lawmakers.

Gov. Mark Dayton and top Republicans were in stop-and-start talks with no word on progress. Six previous straight days of negotiations, following a six-month impasse over how to solve a $5 billion deficit, failed to produce a breakthrough.

Though plenty of states have divided government and almost all have budget problems, Minnesota stands alone on the brink of a shutdown, thanks to Dayton’s pledge to raise taxes on the wealthy to fix the budget and Republicans’ determination to avoid new taxes and instead cut spending to balance the state’s finances. The shutdown would be Minnesota’s second in six years as the partisan divide deepens.

Republican Senate Majority Leader Amy Koch declined to comment on her way into the first budget talk session of the day. “Sorry, guys,” she said as she walked past a crowd of reporters and photographers.

Some citizens rushed to get driver’s and fishing licenses before the shutdown, and state parks were preparing to tell campers to leave as early as Thursday afternoon. The shutdown also would postpone non-emergency road construction, shut the state zoo and Capitol and stop child-care assistance for the poor. More than 40 state boards and agencies would go dark.

The shutdown wouldn’t halt critical services, including the State Patrol, prisons and disaster response.

In Afton State Park, east of St. Paul, Karen Weis and her children and relatives were starting to pack up their camp in case they needed to leave. Weis, a nurse from Austin, said they hadn’t known about the possible shutdown when they scheduled the trip in March.

“If we have to leave early, we have to leave early,” she said. “It’s such a glorious place to be.”

The looming shutdown is the latest — and most frantic example — of a state dealing with the recession’s lingering effects, a fiscal crisis and polarized politics. Here, as in 21 other states, there’s no way to keep government operating past the end of a budget period without legislative action, according to the National Conference of State Legislatures. Even so, only four other states — Michigan, New Jersey, Pennsylvania and Tennessee — have had shutdowns in the past decade, some lasting mere hours.

This shutdown also could also touch more people than Minnesota’s 2005’s partial closure, which affected a few major state agencies and about 8,000 state employees. It lasted eight days before then-GOP Gov. Tim Pawlenty — who is currently waging a White House bid — compromised on a budget with a divided Legislature.

The latest budget dispute started in January, when Dayton became the state’s first Democratic governor in 20 years and Republicans took over the Legislature for the first time in 38 years.

Republicans swept to power campaigning against tax and spending increases, while Dayton won on a message of raising taxes on the highest earners. A five-month legislative session and intermittent negotiations since adjournment last month have produced no visible progress.

Republicans have been pressing Dayton to call a special session so they can pass a “lights on” budget bill to keep government operating past 12:01 a.m. Friday, when a shutdown would start, but the governor has resisted that approach.

“This is going to be a tough shutdown, and people will notice,” David Lillehaug, Dayton’s attorney in the case, said Wednesday. “Anyone who says that government doesn’t do anything and doesn’t do it well, upon reading this order … they’re going to realize they’re very, very wrong.”

Dayton and top Republicans stopped talking publicly about their negotiations days ago, saying they didn’t want to jeopardize any progress. After breaking for the last time Wednesday night, Geoff Michel, the second-ranking Republican in the Senate, said the two sides were “very close” but provided no further details.

With the politicians mostly silent, the most significant development Wednesday came from Ramsey County Chief Judge Kathleen Gearin. She weighed arguments from several parties on which services should be maintained in a shutdown, and ultimately sided mostly with Dayton’s minimalist list.

Gearin found that some programs, such as child care aid programs not directly tied into the federal welfare system, were important but did not rise to the level of critical services. The judge said state payments to cities, counties and schools would continue, as would enough money to keep Dayton’s office and the Legislature running with at least skeletal crews. She ordered that the state keep welfare, food stamp and Medicaid health care programs operating.