Earlier in the week, House Speaker John Boehner circulated a memo telling members "there will be no spiking of the ball" if the law is struck down.
Boehner called for pursuing step-by-step reforms. Cassidy, too, said Republicans would pursue a replacement law whether or not the Supreme Court upholds the overhaul.
He complained that the law has not curbed the rise in health care costs, and called for a plan to achieve that.
Democrats issued a memo of their own this past week, pointing out that several popular provisions of the bill, such as the prohibition on lifetime coverage limits and the ability for young people to stay on their parents' insurance until age 26, are already in effect.
President Obama, speaking Friday to an audience of Latino officials in Florida, also defended the law -- saying it was "wrong" to allow insurance companies to raise premiums at will and "right" to make health care available to all Americans.