Many observers left last week’s contraceptive coverage oral argument at the Supreme Court convinced that the court was headed to a 4-4 tie, with Justice Anthony Kennedy siding with the religious objectors opposing the Obama administration’s plan to cover their female employees’ contraception. On Tuesday, less than a week after oral argument, the court surprised everyone with a two-page order asking the parties for more information on their positions.

“The parties are directed to address whether contraceptive coverage could be provided to petitioners’ employees, through petitioners’ insurance companies, without … notice from petitioners,” the order read in part. It asked for additional briefs due from the plaintiffs by April 12 and from the government in response by April 20.

“This is a twist I did not expect,” said Brigitte Amiri, senior staff attorney at the American Civil Liberties Union, which filed a brief in support of the Obama administration.

Advocates for contraceptive access were cautiously optimistic at the order, which suggested that days after the court’s conference to take an initial vote on the case, it would not easily dispense of the case with a deadlock — as it did in a union dues case Tuesday.

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At the same time, an attorney for several plaintiffs, Mark Rienzi of the Becket Fund for Religious Liberty, called the court’s request an “excellent development. Clearly the Supreme Court understood the Sisters’ concern that the government’s current scheme forces them to violate their religion. We look forward to offering alternatives that protect the Little Sisters’ religious liberty while allowing the government to meet its stated goals.”

At issue is the “accommodation” the Obama administration offered to religiously affiliated nonprofits that object to the contraceptive coverage required under the Affordable Care Act. For-profit corporations like Hobby Lobby, which two years won its bid to be considered a religious objector at the Supreme Court, have been offered the same plan. The employers who object to paying for contraception can notify their insurer or their government of their belief, after which the female employees get their coverage directly from the insurer without financial contribution from the employer. The plaintiffs, which include universities, a nursing home chain run by the Little Sisters of the Poor, and hospitals, say that is still “hijacking” their plans for a violation of their religious beliefs.

Tuesday’s order seems to follow up on a question Justice Elena Kagan asked at oral argument: ”Is there any accommodation that the government would offer that would in fact result in women employees of your clients, or students of your clients, getting health care as part of an employer-based plan or a student-based plan, getting contraceptive coverage? Is there any accommodation that would be acceptable?”

The plaintiffs’ attorney, Noel Francisco, did not quite answer. “Your Honor, possibly so, possibly not, and if I could explain,” he said. “We’ve not been offered that kind of alternative to consider.”

Several attorneys who filed briefs in support of the Obama administration’s position also found the order baffling, because it seemed to ask if the plaintiffs would accept an alternative that, in Amiri’s words, “describes something very much like the accommodation.” But, she added, it’s possible the justices want that clarified. “There were certainly some questions at oral argument that showed some confusion about how insurance worked,” she said. “Possibly when we see the briefs, the government will be more explicit about how things work with the existing accommodation.”

The plaintiffs had pointed to alternative means that women could get contraceptive coverage without involving their health plans, such as through the Title X program for uninsured women or with contraceptive-only plans on the Affordable Care Act exchange. The order suggests the court isn’t necessarily accepting those alternatives.

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“It could mean that there is recognition among the justices of the importance of employees getting this coverage through their regular insurance company,” said Gretchen Borchelt, vice president for reproductive health and policy at the National Women’s Law Center. “That to me is positive movement since oral argument, given the discussion then of ridiculous alternatives like the nonexistent contraceptive-only policy.”

Indeed, put on the spot, the religious objectors may have to provide an answer that doesn’t satisfy Kennedy, who has previously said he thinks women’s access to contraception is a compelling government interest. “The religious objectors are now in a bind,” said Gregory Lipper, senior litigation counsel at Americans United for Separation of Church and State, who co-authored a brief supporting the policy. ”If they say that there is no such way for women to get that type of coverage — even if they don’t have to sign anything —then it becomes even clearer that they are trying to block the independent actions of third parties, and that they don’t want their employees and students to get seamless contraceptive coverage from any source.”

With the new round of briefing, it now seems even likely that a decision will come near the end of the Supreme Court’s term, traditionally the end of June.