The Obama administration thought it had found a way to ease mounting objections to a requirement in the new health care act that all employers — including religiously affiliated hospitals and universities — offer coverage for birth control to women free of charge.

It would make the insurers cover the costs, rather than the organizations themselves.

But the administration announced the compromise plan before it had figured out how to address one conspicuous point: Like most large employers, many religiously affiliated organizations choose to insure themselves rather than hire an outside company to assume the risk.

Now, the organizations are trying to determine how to reconcile their objections to offering birth control on religious grounds with their role as insurers — or whether there can be any reconciliation at all. And the administration still cannot put the thorny issue to rest.

“We’re all kind of waiting and seeing,” said Jim Liske, chief executive of the Prison Fellowship, a Christian charity that insures itself and objects to offering the morning-after pill to its employees.