A majority of states — 33 of them — are now controlled by a single party, and some of those also hit budget impasses this year. But provisions in many of those places, such as extending funding at current levels or setting temporary budgets until deals can be made, have spared residents, for the most part, from the effects.

In Wisconsin, where Republicans control the governor’s office and the State Legislature, disagreements over transportation funding have slowed lawmakers. In Rhode Island, which is entirely under Democratic control, the House has yet to vote on a $9.2 billion budget plan passed by the Senate on Friday. And in Oregon, Gov. Kate Brown, a Democrat, and the Democratic-leaning Legislature have sparred over how the state taxes businesses, but lawmakers appeared to be headed toward an agreement this week.

In states like Maine, however, the effects were immediate. Though state parks and emergency services were kept open, motor vehicle offices were closed, as was the lottery office. And the operations of agencies like the Office of Child and Family Services and the Department of Labor were curtailed, as thousands of workers were idled and lawmakers edged toward a deal.

“Days like today, we regularly have caseworkers that would go out to check on the children,” said Dean Staffieri, the vice president of a state employees’ union and a supervisor in a child protective services office, which he said had only a small crew on call for emergencies on Monday.

For residents, the state’s first shutdown in decades was jarring. Danielle Sirois, a cashier at a Christmas Tree Shops store in Augusta, said she worried for the families of state employees. “I think they should all come together,” Ms. Sirois said of Maine’s lawmakers. “The world is scary to me right now because everybody is so at odds.”

Maine’s combative governor, Mr. LePage, said he would allow state employees to take a day of paid leave on Monday, but many of the workers gathered at the State House wondered how he could do that when there was no budget in place.

By the end, the fight centered on Mr. LePage’s vow not to sign a budget this year with tax increases.