President Obama's top aide addressed the latest controversy over contraception coverage, saying on CBS News' "Face the Nation" Sunday that the latest iteration of the new rule will go forward.

Obama walked back on a policy that would have forced religious-affiliated institutions such as universities and hospitals to cover contraceptives in their employee insurance plans, saying Friday that those institutions will be allowed exemptions.

Under the amended law, religious organizations will not be required to provide contraceptive coverage, pay for it, or refer employees to places that would offer it. The onus will be placed on the employers' insurance companies, who will be required to offer women contraceptive coverage directly and free of charge if their employer will not.

The compromise was not enough for Catholic bishops and Republicans, who called for Obama to renounce the rule completely.

"There's no compromise here," GOP candidate Rick Santorum said. "They are forcing religious organizations, either directly or indirectly, to pay for something that they find is a deeply, morally, you know, wrong thing. And this is not what the government should be doing."

Republicans have introduced legislation in the Senate that would allow any organization--religious or not--to opt out of providing birth control coverage on moral grounds. Senate Republican leader Mitch McConnell said Sunday he's pushing for a vote on the legislation.

House Budget Committee Chairman Rep. Ryan Paul said there are enough votes in the House to pass similar legislation.

A recent poll by the Public Religion Research Institution has found that a majority of Americans agree that "employers should be required to provide their employees with health care plans that cover contraceptives and birth control at no cost."

The Obama administration is including contraceptive coverage under the umbrella of "preventative services," which the Affordable Care Act will require insurance companies to cover without co-pays or deductibles. Many women use the pill for health reasons unrelated to pregnancy prevention.