About three dozen Catholic bishops who gathered in Washington, D.C., for a high-level meeting this week face a tough question in their ongoing standoff with President Barack Obama over contraception and health care: What’s next?

Having waded into a fight on Capitol Hill over federal health care mandates to cover the cost of birth control, the bishops essentially have two choices: confrontation or negotiation.

Both are on the table. Catholic leaders are weighing legal action, said a spokesman for the United States Conference of Catholic Bishops. Additional meetings with the administration also remain possible, but the fight over contraception mandates in the new health care law has become acrimonious and politically charged.

For the bishops, both options present risks. The fight over contraception mandates in the Patient Protection and Affordable Care Act has spotlighted Catholic clout inside the Beltway, where the White House was forced to rewrite regulations in the new law to give religious providers of health care a layer of insulation from directly paying the cost of birth control as part of health care plans.

But the flare-up has also exposed rifts between the Catholic bishops and many Catholic institutions, as well as Catholic voters, who remain an unpredictable bloc.

The extent of the Catholic lobby is notoriously hard to measure, given exemptions in lobbying and IRS disclosure rules for religious institutions.

The U.S. Conference of Catholic Bishops spent about $26.7 million on advocacy and lobbying in 2009, an almost $1.4 million increase over 2008, according to the Pew Research Forum on Religion & Public Life.

The U.S. Conference of Catholic Bishops disputed that number, saying it was exaggerated. The study’s author acknowledged the challenge of pinning down an exact number but noted that the group’s total budget is about $143 million.

Whatever the bishops spend on advocacy and lobbying, there’s little question they’ve raised their Washington, D.C., profile and responded aggressively to the health care mandate. Last fall, the bishops set up a special Ad Hoc Committee on Religious Liberty, headed by Bridgeport, Conn., Bishop William Lori, who quickly became a popular GOP witness on Capitol Hill.

“It’s a much more orchestrated and efficient organization,” said Barry Lynn, executive director of Americans United for Separation of Church and State.

Health and Human Services regulations initially exempted houses of worship but not religious institutions such as hospitals and universities, prompting a nationwide outcry from the bishops. Cardinal Timothy Dolan, president of the U.S. Conference of Catholic Bishops and archbishop of New York, called the mandate “literally unconscionable.”

Hundreds of U.S. bishops decried the mandate as a violation of religious freedom, from the pulpit and in letters and public statements, and Catholic leaders worked to forge a compromise with the administration. Even Pope Benedict XVI weighed in, voicing concern over attempts “to limit that most cherished of American freedoms, the freedom of religion.”

Last month, the administration announced that insurance companies, not religious institutions, would bear the cost of the mandated birth control coverage, but the Catholic bishops remain dissatisfied. They sent letters to Capitol Hill trying to win approval for an amendment by Sen. Roy Blunt (R-Mo.) that would have effectively rolled back the mandate for religious institutions, but the Senate rejected it.

Now bishops from all over the country are gathered at the headquarters of the U.S. Conference of Catholic Bishops for a meeting of the group’s elite administrative committee. Though the meeting’s agenda for today and Wednesday has not been released, the mandate was widely expected to be front and center.

There are signs that the bishops are eager to rally their flock behind them. The bishops have reissued an action plan dubbed “Forming Consciences for Faithful Citizenship,” which describes itself as “a call to political responsibility.” Dolan reportedly told a recent diocesan convention in New York: “We are called to be very active, very informed and very involved in politics.”

It’s unclear whether the Catholic flock will follow, however. Polls show that most Catholics believe Americans should have access to birth control and contraception and that they largely support the administration’s health care compromise.

“The polling clearly shows that the Catholic voters do not follow the bishops’ line on social issues,” said Jon O’Brien, president of Catholics for Choice. Several Catholic institutions, including the Catholic Health Association of the United States and the University of Notre Dame, came out in support of the administration’s compromise.

Increasingly, Catholics vote as a bloc within a couple of points of the population at large, say political analysts, possibly diluting their sway. The more relevant voting bloc in 2012 may well be women. Recent health care and contraception controversies have played to Democrats’ advantage, polls suggest, and the Obama campaign has moved quickly to seize its opening.

A key issue for the Catholic bishops is whether the contraception controversy is framed as a matter of health care policy or religious freedom, said political scientist Allen Hertzke, who authored the Pew report on religious advocacy.

“Will it be access to birth control, or will it be the threat to religious conscience rights?” asked Hertzke, a professor of political science at the University of Oklahoma. For Catholic bishops, the issue is clearly a matter of religious freedom. It remains to be seen whether rank-and-file Catholics agree.