More than half of the nonprofit health insurance co-ops formed through the Affordable Care Act are now off the market for the coming year, with the last-minute departure of a plan in Michigan.

On Tuesday, two days after the start of the new enrollment season in insurance exchanges created under the health-care law, the Web site of Michigan’s Consumers Mutual Insurance posted notice that it will not sell coverage for 2016.

That co-op becomes the 12th plan to fail in the past year — and the ninth this fall — out of the 23 that opened at the start of 2014. The plans have offered an alternative, consumer-oriented type of coverage that the ACA envisioned as competition for traditional health insurers.

The dozen collapses will disrupt insurance for 740,000 individuals and small-business employees, who are being instructed by state and federal officials to choose new plans in time for them to take effect in January. In New York state, the window is narrower. Government officials have moved up the closing date of the New York Health Republic co-op, the nation’s largest, giving its more than 200,000 members just two weeks to select different coverage before it shuts down at the end of this month.

The latest gyrations are occurring as the co-ops become new fodder for the partisan acrimony that has surrounded the 2010 law since its beginnings. At a hearing Tuesday afternoon of a House Ways and Means subcommittee, Republicans accused the Obama administration of wasting taxpayers’ money on an aspect of the law that they say is failing. Democrats countered that a series of GOP-forced budget cuts crippled many co-ops’ chances to thrive.

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In Michigan, the co-op’s departure from the marketplace is the first that has not been accompanied by any public closure announcement. Michigan insurance regulators are working with Consumers Mutual on a “wind-down plan.”

State officials there are being far more secretive than their counterparts across the country have been as other co-ops have collapsed. The only visible signal is the plan’s disappearance from the insurance offerings available there through HealthCare.gov, the ACA’s federal enrollment system.

“Our financial oversight is confidential,” said Judy Weaver, senior deputy director of the Michigan Department of Insurance and Financial Services. “We are not allowed to talk about our companies.”

Dennis Litos, Consumer Mutual’s chief executive, said that it is in discussions with state insurance officials “on a wind-down plan. We hope to conclude on the plan this week.”

The discussions, Litos said, focus on various strategies for discontinuing health insurance for individuals and small businesses. According to the co-op’s figures, it has about 27,500 members. Nearly 6,000 of them have gotten coverage through HealthCare.gov.

Meanwhile, in Arizona, a co-op that just days ago was ordered to fold by regulators is resisting. The state’s insurance director, Andy Tobin, announced on Friday that he was placing Meritus Health Partners under state supervision and closing it down. His statement also said that the co-op “declined to consent” to that order.

Meritus chief executive Tom Zumtobel said Tuesday that the co-op’s board is “still assessing our options” and has not given up on the idea of trying to get back on Arizona’s exchange. Still, callers to Meritus’s main phone number get a recording that the state has taken it over and that it is unavailable for 2016 health-care coverage.

The House hearing on the co-ops maintained the drumbeat of ACA opposition by Republican members, who have voted more than 50 times to repeal the law.

“A model that is wrong isn’t going to succeed,” the subcommittee’s chairman, Rep. Kevin Brady (R-Tex.), said as he accused administration health officials of “poor decision-making and failed execution.”

Other committee members singled out recent efforts by officials to help prop up some co-ops’ finances by converting federal start-up loans, due to be repaid within five years, to longer-term loans.

Several asked the hearing’s witness, Mandy Cohen, chief of staff for the Centers for Medicare and Medicaid Services, how much money the government would be able to recover from loans made to co-ops that are going out of business.

“We are going to be using every tool available to recover taxpayer dollars,” Cohen replied, though she declined to predict a dollar amount.

The subcommittee’s ranking Democrat, Rep. Jim McDermott (Wash.), charged that Republicans “have deliberately sabotaged” the co-ops, slashing their initial funding from $6 billion to $2.6 billion. The GOP has “weakened and undermined the co-ops at every turn,” McDermott said. “Now they point the finger at the administration when they fail.”

Also on Tuesday, federal health officials announced that they were introducing a feature on HealthCare.gov on an experimental basis: a tool that will let insurance-shoppers search which ACA health plans in their area cover the doctors and health-care facilities they prefer. A similar feature, allowing consumers to search for plans that cover the medicine they take, is still not available.