After facing a Supreme Court defeat over contraception this week, the Obama administration is considering various ways on how to provide coverage for contraception for thousands of women who will lose coverage due to employers' religious beliefs.

According to The New York Times, legal experts expect many employers to take cases to court to take advantage of the decision involving Hobby Lobby, which affects for-profit businesses, and the decision involving Wheaton College, which applies to religiously-affiliated nonprofit groups. The decision allows the businesses and nonprofits to opt out of providing contraception insurance to female employees.

The Obama administration is considering one proposal that would put the burden of contraception insurance on companies' insurers or health plan administrators, with details of reimbursement to be figured out later.

Another method would give the Obama administration a bigger role in offering free coverage to women who cannot get it through their employers, although a government entitlement program is not as viable due to fiscal constraints.

The administration is under so much pressure that the details of how the proposed programs will be administered or financed have not been worked out. However, officials from the administration have said they are determined to provide broad coverage of contraceptives to the largest number of women possible without requiring employers to provide contraception if it is against their beliefs.

While some legal experts say the government can provide an alternative proposal, Justice Sonia Sotomayor said that the challenge facing the federal government in providing coverage to women is "daunting -- if not impossible."

The administration is also hoping to implement a new plan in order to acquire more women supporters ahead of the November midterm elections. The Democratic National Committee is already telling voters to protest the Hobby Lobby decision.

Previously, the administration had an arrangement that allowed religious nonprofits to fill out a form that transferred the delivery of the free coverage under the Affordable Care Act to others.

However, some religious nonprofits do not want to even sign the opt-out form, as they believe even that is morally wrong. Many organizations consider all forms of contraception immoral, while some, such as Wheaton College, a Christian liberal arts college in Illinois, are against the morning-after pill, as they believe it enables abortions. The Supreme Court granted a temporary exemption in the ruling for the college, which was decided Thursday.

Justice Ruth Bader Ginsburg and Elana Kagan joined Justice Sotomayor's dissent in the ruling. Three days earlier, Justice Stephen G. Breyer joined the three female justices in dissenting in the 5-4 ruling.

The court's conservative majority, who are all men, believed that the administration can find other ways to deliver coverage for birth control.

The court also said that Wheaton can notify the government of its religious objection in writing rather than send to the opt-out form to health insurance providers. While it seems like a small difference, Justice Sotomayor said in her dissent that it creates problems for the Department of Health and Human Services.

"Does the court intend for H.H.S. to rely on the filing of lawsuits by every entity claiming an exemption?" she asked.

Yet, Wheaton said it will not have a problem sending a notice to the H.H.S.

The decision differs from the Affordable Care Act, which has allowed millions of women to have access to birth control without co-payments or additional charges. However, the administration has since fought with religious organizations, including priests and nuns, over the details of health insurance coverage.

During this week's decision, Justice Alito wrote that he agrees with shifting contraceptive costs to insurance companies, as organizations will not have to violate their religious beliefs.

The idea of shifting insurance costs will require insurance companies and plan administrators to deliver coverage when they are notified about an employer's religious objections. Insurance companies will then bear the costs, or receive reimbursement from the federal government.

If employers self-insure, the administration said plan administrators can get a "compensating reduction" in the fees paid by insurers to participate in the insurance exchanges under the Affordable Care Act.

However, that way, insurers and third-party administrators have to pay the bill for contraceptive coverage without immediate reimbursement.

The Obama administration said that the cost of providing birth control will be offset by savings acquired from the increased use of birth control.