But Romney has drawn criticism from his GOP rivals and the White House over policies when he was Massachusetts governor.
In late 2005, Romney required all Massachusetts hospitals, including Catholic ones, to provide emergency contraception to rape victims. Some Catholics say the so-called morning-after pill is a form of abortion.
Romney said he did not support the Massachusetts law, which passed despite his veto. But he also said at the time, "My personal view, in my heart of hearts, is that people who are subject to rape should have the option of having emergency contraception or emergency contraception information."
White House spokesman Jay Carney seized on that policy at his daily briefing Wednesday.
"The former governor of Massachusetts is an odd messenger on this given that the services that would be provided to women under this rule are the same services that are provided in Massachusetts and were covered when he was governor," Carney said.
He called it "ironic that Mitt Romney is criticizing the president" for a policy that Carney described as identical to the one in place in Massachusetts.
Boehner said that if the administration fails to reverse the policy, then Congress will act. He said that in the coming days, the House Energy and Commerce Committee will move ahead on legislation.
A group of House Democratic women sought to frame the issue in economic and health terms, arguing that birth control reduces health costs and stops unintended pregnancies.
In a conference call, Rep. Lois Capps, D-Calif., who said she spoke as a nurse, mother and grandmother, pointed out that 28 states have similar rules on coverage for birth control. Schakowsky pointed out that the rule affects nurses, secretaries and janitorial staff who may not be Catholic.
Rep. Gwen Moore, D-Wis., said the church "can't impose its religious views on people and whether they can have health care."
But not all Democrats backed the administration. Tim Kaine, a Catholic seeking the Senate seat in Virginia, said he supports contraceptive coverage but thinks there should be a broader exemption for religious organizations. He made the comments in a radio interview Tuesday with the "HearSay with Cathy Lewis" program on WHRV in Hampton Roads, Va.
Sen. Joe Manchin, D-W.Va., who faces re-election in November, sent a letter to Obama complaining that the mandate is a "direct affront to religious freedoms."
Rep. Dan Lipinski, D-Ill., said in January that the decision "violates the long-standing tradition of protection for conscience rights in federal law."
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.