By Elise Viebeck - 09/30/13 04:15 PM EDT
The policy has been challenged in more than 70 lawsuits from religious institutions dissatisfied with moves to accommodate their objections as well as secular companies with religious owners.
Democratic women senators and groups that support the mandate denounced the House's move to weaken it.
"This version of the CR would allow bosses to impose their religious beliefs on the women who work for them by blocking women’s access to preventive health are for broad and undefined ‘moral’ reasons," said National Women's Law Center Co-President Marcia D. Greenberger in a statement.
"Women are more than capable of making their own health decisions and have a right to do so without interference from their bosses or members of Congress."
The Center for Reproductive Rights also blasted the House-passed provision.
The House GOP is "far more interested in using the threat of a government shutdown to hold women’s access to affordable birth control hostage than in passing a federal spending bill," said President and CEO Nancy Northup in a statement.
"We shouldn’t have to keep repeating over and over that it’s downright un-American to have your healthcare depend on what your boss happens to approve."
The ObamaCare mandate is designed to ensure that most working women have access to free birth control in their health plans.
It includes several exemptions and work-arounds for explicitly religious institutions.
Churches and houses of worship can ignore the rules, while religiously affiliated employers will not be required to pay for, offer or facilitate birth control coverage themselves.
Opponents of the policy argue that offering coverage for drugs they object to violates their religious freedom.