The Obama administration's revised ruling on the contraception coverage that religious institutions must offer employees has not won over critics, despite granting those religious institutions extended exemptions.

On Sunday morning, Rep. Paul Ryan (R-Wis.) joined the chorus, calling the new policy -- which allows church-affiliated schools and hospitals to punt the cost of contraception coverage to the health care insurers -- insufficient.

"It's a distinction without a difference," Ryan said on ABC's "This Week." "It's really an accounting trick. It forces the insurance company that they have to pay to do the coverage. So instead of making the institution itself, it reinforces the insurer. And a lot of these Catholic institutions are self-insured, and all insurers under this rule must provide these mandated benefits. So it really is a distinction without a difference. This should be rescinded, not compromised like this, because I would, again, say it's not a compromise. The president's doubling down."

Earlier in the interview, the Wisconsin Republican insisted that the GOP had the votes to block the contraception rule from going forward, likely in the form of legislation that would overrule it.

Ryan is a practicing Roman Catholic, but he's known primarily as a budget wonk. That he would criticize the policy change as insufficient underscores how convinced the GOP is that this issue is a winning one, both on religious freedom grounds and matters of federal government power.

That said, the White House seemed fairly insistent on Sunday that neither a rescinding of the policy or future changes were forthcoming.

"We have set out our policy," the president's chief of staff, Jack Lew, told "Fox News Sunday," when asked if more alterations were forthcoming. "We are going to finalize it in the final rules, but I think what the president announced on Friday is a balanced approach that meets the concerns raised both in terms of access to health care and in terms of protecting religious liberties, and we think that's the right approach."

Lew repeated the line during a sit-down with CNN's State of the Union:

CANDY CROWLEY: So no more compromising? LEW: We've put out the plan that reflects where the president intended to go. CROWLEY: So that means there is room for compromising or is not? LEW: No. This is our plan.