ABC

House Budget Committee Chairman Paul Ryan, R-Wis., shot down the Obama administration's compromise on contraception Sunday, discounting the plan that requires insurance companies, instead of religious hospitals or universities, provide access to free birth control under the new health care law as nothing more than an "accounting trick."

"This thing is a distinction without a difference," Ryan told me Sunday on "This Week."  "It's an accounting gimmick or a fig leaf.  It's not a compromise."

Ryan said Republicans "absolutely" have enough votes in the House to block Obama's plan, which the White House announced on Friday.

The plan comes after a tumultuous week of tension between the Catholic Church and the Obama administration over a newly announced rule that faith-based hospitals would not be exempted from providing co-pay-free contraception to their employees despite the church's adamant objections to birth control.

Ryan said that because some Catholic institutions are self-insured, the compromise does not solve the problem, as those faith-based intuitions would still have to provide services that run counter to their religious beliefs.

"This should be rescinded, not compromised like this, because I would, again, say it's not a compromise," Ryan said. "The president's doubling down."

But White House Chief of Staff Jack Lew insisted the administration would push forward with the plan.

"We didn't expect that there would be universal support, but we do think this is the right way to go, and it's a plan that we're going to pursue," Lew told me on Sunday.

"Most importantly," Lew added, "this will guarantee that every woman has a right to preventive care, including contraceptives, and no church will be required to provide the benefit, and no Catholic university or Catholic hospital will either have to pay or facilitate the provision of the benefit.  It will come from the insurance companies."

Organizations on both sides of the debate came out in support of the president's compromise plan on Friday. Both Planned Parenthood and the Catholic Health Organization said they were pleased with the administration's solution.

But on Saturday the U.S. Conference of Catholic Bishops denounced the plan, saying in a letter that "it does not meet our standard of respecting the religious liberty and moral convictions of all stakeholders in the health coverage transaction."

The bishops expressed concern that the cost of providing free contraception could fall to the religious institutions in the form of higher premiums for employee health insurance.

Lew insisted that providing contraception would not increase costs.

"If you look at the overall cost of providing health care to a woman, the cost goes up, not down, if you take contraceptives out," Lew said. "If anything, [the president's plan] could save money over time."