But Moore said this change goes against a promise made by Democrats and President Obama that people who like their current coverage can keep it.

"This would mean that millions of women — contrary to what we have promised them through the affordable Care Act, that they would be able to keep coverage they currently have — would actually lose the coverage that they currently have," Moore said.

Moore added that the bill would endanger women's lives by shutting off abortion services and even information about these services.

"It's not hyperbole to say that the provisions of the Pitts bill represent an extreme and callous attack on women's health," she said.

Among other things, she said the bill would allow people with tangential relationships to health providers, such as receptionists, to refuse services to people seeking abortions. She said it would also allow hospitals to deny coverage.

"Hospitals would no longer be forbidden from abandoning patients on the doorstep of emergency rooms and providing treatment to at least stabilize the medical condition of such patients," she said.