The delay marks a setback for President Donald Trump, who campaigned on a promise to repeal and replace the Affordable Care Act.
"You don't just have an abortion and leave," one woman says as Republicans threaten to defund Planned Parenthood.
Republicans are divided over the plan, with Senate moderates concerned it goes too far and House conservatives saying it does not go far enough.
The CBO, a nonpartisan congressional agency, forecast on Monday the plan would increase the number of Americans without health insurance by 24 million.
The Kentucky senator reintroduced legislation that Republicans put on former President Obama's desk last year.
House Republicans have revealed their long-awaited replacement for Obamacare. Here, a health care economics expert offers a tour of the new legislation.
Attacks on health care facilities have resulted in an increase in deaths from preventable diseases, the report says.
A new report finds Obamacare gets high marks in conservative states where more low-income individuals now have health insurance.
President also orders an immediate regulatory freeze for all government agencies.
Most Americans think repealing it without a replacement is a bad idea, polls show, but there are some who are steadfastly against it.
Trump said he wanted a substitute for President Barack Obama's healthcare law done "very quickly or simultaneously" to the vote to get rid of it.
The new head of the Department of Health and Human Services could repeal the Affordable Care Act and restructure Medicare and Medicaid.
Denying patients the best cures because the insurers don't want to foot the bill is callous and counterproductive.