Catholics approval of President Barack Obama has remained relatively unchanged despite facing harsh opposition from the U.S. Conference of Catholic Bishops over new contraception rules.

A survey released Tuesday by Gallup found that 46 percent of Catholics approved of Obama last week. A week prior to that his approval was at 49 percent, a change within the margin of error.

"Catholics are typically an important swing voting group in U.S. elections, so a president is at some political risk if he pursues a policy that could anger Catholics," Gallup explained. "So far, though, it appears the controversy over religious group employer health plans and contraception has not had a significantly negative effect on how rank-and-file Catholics view the president."

"One key will be whether Catholic approval of Obama stays a bit lower than it has been in the coming days or begins to edge back closer to 50 percent, where it had been earlier this year."

Obama had proposed new U.S. Department of Health and Human Services rules to require private health insurance plans to cover contraception for women, without an exemption for religious employers.

Facing a backlash from Catholic bishops and their Republican supporters, the White House said last week that it would change the proposed rules by exempting religious hospitals and universities, and instead mandating that insurance companies provide those services.

But the U.S. Conference of Catholic Bishops still fiercely opposes the proposed rules, saying the “mandate of insurance coverage of sterilization” was a “needless government intrusion in the internal governance of religious institutions.”

However, the Catholic Health Association, Catholics United, the University of Notre Dame, the Association of Jesuit Colleges and Universities, and Catholic Charities USA all approved of Obama's compromise.