Updated 6:23 p.m. ET, 12/31/2013
Washington (CNN) – A group of Catholic organizations, in an emergency appeal on Tuesday, asked the Supreme Court to delay the Obamacare requirement that certain religious-affiliated groups provide contraception and "abortion-inducing drug" coverage to their workers.
Archdioceses in Washington, D.C., Tennessee and Michigan - along with affiliated groups that include Catholic University - asked Chief Justice John Roberts and Justice Elena Kagan to block enforcement of the employer mandates under the Affordable Care Act set to take effect on Wednesday.
The issue has been a major sticking sticking point with religious groups and private for-profit companies that have strong moral objections.
Under final rules negotiated between the administration and a variety of outside groups, churches and houses of worships are exempt from the mandate.
But other non-profit religious-affiliated groups like church-run hospitals and parochial schools must either provide no-cost contraception coverage or have a third-party insurer provide separate benefits without the employer's direct involvement.
"Tomorrow, applicants (the Catholic organizations] will be forced to choose between onerous penalties or becoming complicit in a grave moral wrong," according to the court filing from the groups.
"Just as an individual may be held accountable for aiding and abetting a crime he did not personally commit, so too may a Catholic violate the moral law in certain circumstances by cooperating in the commission by others of acts contrary to Catholic beliefs.
"For some, religion provides an essential source of guidance both about what constitutes wrongful conduct and the degree to which those who assist others in committing wrongful conduct themselves bear moral culpability," the groups said.
There was no indication when Roberts, Kagan or the high court as a whole would rule.
The appeal came after the president of the U.S. Conference of Catholic Bishops, Archbishop Joseph Kurtz of Louisville pressed President Barack Obama on the issue.
He asked Obama in a letter that went further than the appeal to Roberts and Kagan to exempt some businesses and religious-affiliated institutions from enforcement of the mandate - through fines - until the Supreme Court rules on the matter.
He pointed to other delays the administration has made in the law, such as putting off until 2015 the requirement for all employers with more than 50 workers to provide health coverage.
But Kurtz notes that "an employer who chooses, out of charity and good will, to provide" health insurance for employees can still face fines if that employer does not want to comply with the contraception requirement.
"In effect, the government seems to be telling employees that they are better off with no employer health plan at all than with a plan that does not cover contraceptives," he writes.
The letter represents a major first act by Kurtz, who was elected president of the bishops' conference in November, succeeding Archbishop of New York Cardinal Timothy Dolan.
The Supreme Court agreed last month to hear two cases involving for-profit corporations who say their religious liberty is violated by the law.
Among the plaintiffs is Hobby Lobby, Inc. nationwide chain of about 500 arts and crafts stores.
At issue is whether private companies can refuse to do so on the claim it violates their religious beliefs.
The privately held company does not object to funding all forms of contraception – such as condoms and diaphragms – for their roughly 13,000 employees, which Hobby Lobby says represent a variety of faiths.
The Green family, which owns Hobby Lobby, said in court filings they object to contraceptives like the morning after pill, which they would say constitutes abortion and violates their faith.
Hobby Lobby calculated that their refusal to provide the coverage could result in a fine of up to $1.3 million daily.
The White House said in November that it believes a requirement on contraceptives is "lawful and essential to women's health."
– CNN's Eric Marrapodi and Ashley Killough contributed to this report.