Updated

The standoff between the Obama administration and the Catholic Church intensified Monday, as a leading clergyman freshly urged Catholics and worshippers in other religions to protest a federal policy that the White House indicated it is not inclined to revise further.

"People need to speak up," Cardinal Donald Wuerl, Archbishop of Washington, said during an appearance Monday on the Fox News program "America’s Newsroom."

"There's one thing in the heart of this nation that we're counting on, and that's the basic fairness of the American people."

At issue is a ruling last month by the Department of Health and Human Services mandating that all employers provide free access to contraception for female workers. Devout Catholics oppose the use of contraception and objected to the rule as an attack on religious liberty, arguing the federal government was forcing Catholic-affiliated charities, hospitals and schools to violate deeply held doctrine.

President Obama – who won the Catholic vote in 2008 and was eager to quell a growing controversy as he girds for a tough re-election fight in the fall – announced a modification of the rule on Friday. Under his proposed "accommodation," such Catholic-affiliated organizations would not have to pay for the contraception offered under their employees’ health care plans; instead, the relevant insurance companies would do so.

After initially regarding the president’s announcement with cautious optimism, the U.S. Conference of Catholic Bishops, headed by Archbishop Timothy Dolan of New York, issued a second statement late Friday rejecting it.

"Today's proposal continues to involve needless government intrusion in the internal governance of religious institutions, and to threaten government coercion of religious people and groups to violate their most deeply held convictions," the bishops said. "The lack of clear protection for key stakeholders – for self-insured religious employers; for religious and secular for-profit employers; for secular non-profit employers; for religious insurers; and for individuals – is unacceptable and must be corrected."

It was not at all clear, however, that redressing some of these concerns would end the impasse. "If there is an exemption for Catholic institutions that self-insure," Fox News anchor Martha MacCallum asked Cardinal Wuerl, “do you think that the church's response to the president would then be favorable?"

"We would have to see what that would look like," the archbishop replied. “But even if we were to find some satisfactory conclusion of the question of immoral activities and paying for them, we still have to get to the more basic issue, and that is a fundamental freedom of religious, faith-based groups to carry out their ministry unimpeded by government directives."

Top White House officials, for their part, have suggested the issue is – at least for now – settled.

"So you're not going to change, despite what the bishops say?" Chris Wallace, host of "Fox News Sunday," asked White House Chief of Staff Jacob Lew over the weekend. "Our policy is clear,” Lew replied. "Meaning no revisions to the revisions?" Wallace persisted. "We have set out our policy," Lew answered.

The White House has posted on its website a short list of Catholic-affiliated groups that welcomed the Friday announcement, in varying degrees. They include Catholic Charities, the Catholic Health Association, and Catholics United. Both Catholic Charities and the Catholic Health Association endorsed the president's health care law in 2009.

Today, the White House suggested that political motivations could be driving those still opposed to the revised HHS rule.

"We never set out with the assumption that everyone would be satisfied with this balanced approach," White House Press Secretary Jay Carney told reporters at Monday’s daily press briefing. "And I would simply note with regard to the bishops that they never supported health care reform to begin with."