Mr Duncan Smith has acknowledged the result of the Lords' vote could depend on independent crossbenchers, including leading bishops who have criticised the plans.

BBC: Lord Ashdown to vote against coalition benefits cap

What is the point of giving the pope supreme jurisdiction over the entire Church - including the right to depose bishops - if he never uses it?

BBC: Pope Benedict XVI will step down at the end of the month

The bill was backed by several religious organizations, including the American Jewish Committee, the U.S. Catholic Conference of Bishops, the National Association of Evangelicals and the Jewish Federations of North America.

WSJ: House clears disaster aid for houses of worship

But, late last month, at an emotional mass funeral for 19 victims of the violence, a host of respected Kenyans, including seven Roman Catholic bishops, led angry mourners in heaping blame on the government.

ECONOMIST: Kenya

The U.S. Conference of Catholic Bishops, associations representing Catholic hospitals and schools including the University of Notre Dame didn't immediately offer a substantive response, saying they were still studying the proposals.

WSJ: Obama Health Law Contraception Opt-Out Proposed

In the last several years, church leaders have been trying to shore up the religious identity and mission of organizations that call themselves Catholic, including trying to bar groups from saying they have ties with the church if bishops believe the organizations stray from church teaching.

NPR: Catholic Newspaper Draws Rebuke From Bishop