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Forty-three Catholic groups, including the University of Notre Dame and Archdioceses of New York and Washington, have sued the Obama administration over a controversial mandate requiring employers to offer insurance plans that include contraception coverage.

In a coordinated filing of 12 lawsuits in federal courts across the country, the groups argue that the mandate would unconstitutionally force religiously-affiliated institutions, like Catholic schools and hospitals, to indirectly subsidize contraception for female employees in violation of religious beliefs.

President Obama in February attempted to accommodate the groups' concerns with an administrative compromise he said would ensure no religious organization had to pay for or provide the services directly.  But today's lawsuits signal that the Catholics groups found the effort insufficient.

"We have tried negotiation with the Administration and legislation with the Congress - and we'll keep at it - but there's still no fix," Cardinal Timothy Dolan of New York said in a statement . "Time is running out, and our valuable ministries and fundamental rights hang in the balance, so we have to resort to the courts now."

Catholic officials said one reason behind the decision to file suit was the need to have clarity ahead of decisions about which health plans to provide employees in the coming year, or whether to offer health insurance at all.

One Catholic college in Ohio - the Franciscan University of Steubenville - announced last week that it was discontinuing its health insurance plan because of the contraception mandate.

The lawsuits, which name the U.S. Departments of Health and Human Services, Labor and Treasury, are being coordinated by the high-profile law firm Jones Day, church officials said.

"Let me say very clearly what this lawsuit is not about: it is not about preventing women from having access to contraception, nor even about preventing the Government from providing such services," said Fr. John Jenkins, president of the University of Notre Dame.

"Many of our faculty, staff and students - both Catholic and non-Catholic - have made conscientious decisions to use contraceptives. As we assert the right to follow our conscience, we respect their right to follow theirs. And we believe that, if the Government wishes to provide such services, means are available that do not compel religious organizations to serve as its agents," he said.

"We do not seek to impose our religious beliefs on others; we simply ask that the Government not impose its values on the University when those values conflict with our religious teachings."

The White House declined to comment on the new lawsuits.  But senior Obama campaign strategist David Axelrod suggested support for the president's compromise should be "common sense."

"I think that the administration struck a common sense rule here that doesn't ask these institutions in any way to sponsor contraceptive services for their employees, many of whom aren't catholic, but gives the employees a chance to access those services through a third party," Axelrod told MSNBC. "These institutions don't have to pay for it, don't have to sponsor it. And I think most people agree that's an appropriate compromise."

In a March ABC News/Washington Post poll, Americans were broadly supportive of the regulation in general - 61 percent in favor, 35 percent opposed - but not if religiously-affiliated employers were forced to comply in violation of its religious beliefs. In that case, support dropped to about an even split, 49-46 percent.