For an administration seeking to win a skeptical public over to ObamaCare, the Justice Department could not have picked a more sympathetic foe for a Supreme Court fight than The Little Sisters of the Poor.

The administration is fighting back against a lawsuit filed by the non-profit, which does not meet ObamaCare's classification of a "religious employer"  because it hires and tends to people of all religious and ethnic backgrounds.

Supporters say The Little Sisters of the Poor epitomize service by caring for the elderly poor and those deemed "worthless" by society. In the United States, it runs 30 homes where hundreds of its employees provide nursing and end of life care.

"You know there's a lot of good Catholic organizations out there -- the soup kitchens and the like," says Bill Donahue, president of the Catholic League, "But let's face it, when it comes right down to it in terms of one-on-one personal care, the work that the Little Sisters of the Poor are doing has no parallel."

Because it does not meet ObamaCare's definition of a "religious employer," lawyers for the Little Sisters of the Poor say the organization is not exempt from the contraceptive mandate in the health care law. That means employees are supposed to be provided contraceptive coverage.

It is suing the administration to change that.

In an opposing brief to the Supreme Court, the Justice Department claims the Little Sisters are, in effect, exempt from the contraception mandate. The DOJ says the non-profit has the right to hire a third party to administer coverage and that by signing a simple two-page waiver, the Little Sisters can forego the mandate.

The brief says the Little Sisters are "under no legal obligation to provide the coverage after applicants certify that they object to providing it."

But lawyers for the Little Sisters doubt that. They cite other court papers in which the government has said it is considering other options to enforce the contraception mandate against churches and religious organizations.

Daniel Blomberg, an attorney for the Beckett Fund, which represents the Little Sisters  told Fox News, "The document on its face says when you receive this third party insurer, you have a legal duty to provide these drugs. Now, all the government is saying is, we can't enforce that legal duty. That'd be like the government saying, yeah, the speed limit is 55, but we don't have any police officers who can catch this particular type of vehicle right now."

If the Little Sisters don't sign the waiver, the organization could potentially be fined $4.5 million a year - about a third of its budget.

Last week Supreme Court Justice Sonia Sotomayor granted a temporary injunction preventing the government from enforcing the contraception mandate against the Little Sisters, while it is contested in lower courts. She can extend the injunction herself, or refer it to the whole court for arguments and then a decision would be likely in June.