But Democrats, in particular, said the changes must not weaken protections for patients.
Early proposals were criticized by environmental groups as significantly weakening existing protections for the species.
Many worried that it would weaken protections for Indian women.
The bill would also weaken environmental protections, reducing the opportunity for public appeals and judicial review.
In the first session, the House Republicans voted 191 times to weaken environmental protections.
Democrats say the provisions would weaken Clinton-era protections for national forests.
The other would weaken protections for dwindling fish species.
The measure would have weakened protections and bargaining rights for city workers.
It would weaken special protections for sensitive areas like wetlands.
It also weakens protections that the convention provides for American soldiers who may be captured.