Senator Chuck Schumer of New York, the Democratic leader, called that “a ruse to get to full repeal” and warned that hard-line Republicans in the House would apply pressure to reluctant moderate Republicans in the Senate.

A scaled-down bill would fall far short of what Senate leaders had aspired to pass. But if 50 senators could agree, with Vice President Mike Pence breaking any tie, such a bill would keep alive the effort to repeal the Affordable Care Act, under which about 20 million people have gained coverage.

“What we need to do in the Senate is figure out what the lowest common denominator is — what gets us to 50 votes so that we can move forward on a health care reform legislation,” Tom Price, the secretary of health and human services, said on CNBC.

That strategy would require conservative senators like Rand Paul of Kentucky, Ted Cruz of Texas and Mike Lee of Utah to vote for a measure that leaves the basic structure of the Affordable Care Act in place, hoping that House-Senate negotiations could produce a more ambitious repeal. Such senators have argued that far broader replacement legislation did too little to eradicate the health law.