“We have some very small carriers in the state,” said Susan E. Voss, the Iowa insurance commissioner, who said she favored letting state regulators decide whether some carriers should be given more leeway. The state has already lost some carriers, including the Principal Financial Group, which announced its decision last week.

The new standards may prove a challenge to the administration in its attempt to protect the limited-benefit plans. Under the legislation, insurers are required to spend at least 85 cents of every dollar in premiums on the welfare of their customers, and many of these plans spend far less.

The administration says it has the authority to change the way medical spending is calculated. But the National Association of Insurance Commissioners, which has been charged with drafting the regulations that will go to the Health Department for approval, has so far rejected the notion that these plans deserve special treatment.

A committee looking at the issue concluded that there was no reason to calculate spending differently for these plans, saying state regulators could always request exemptions later if they foresaw too much market turmoil.

Some consumer advocates argue that Congress did not intend for these mini-plans to be unaffected by the new standards. “If they wanted to exclude mini-meds, they would have excluded mini-meds,” said Timothy S. Jost, a law professor at Washington & Lee University who has been working with state regulators on these issues.

And even some state regulators, like Ms. Voss, whose state has formally requested a federal waiver to allow Iowa to decide case by case what considerations to give individual carriers, acknowledges that some plans should be allowed to leave the market. “I don’t think my job as a commissioner is to make sure every company is viable forever,” Ms. Voss said.

The struggle to stop insurers from dropping child-only coverage illustrates the limited power that the administration, and some states, may have to pressure companies to participate. While federal officials have tried to address the concerns by insurers that the rules allow parents to wait until their children are sick to sign up, some insurers have remained reluctant to commit to the market.