The Obama administration has already abandoned the long-term care provisions, known as the CLASS Act, deeming the program financially insolvent when it started last year, Roll Call reported.
Republicans had voted almost immediately after regaining a House majority last year to repeal the healthcare law.
Now, GOP members are expected to hold off on further votes as they wait for the U.S. Supreme Court to begin hearing oral arguments on the law next month.
"We voted to repeal the whole thing. What else can we do?" said Rep. John Shimkus, R-Ill., a member of the Energy and Commerce Committee, which shares jurisdiction over healthcare issues.
With uncertainty over what the high court will do, Shimkus said, "Why spend a lot of time, effort and energy on trying to figure that out when we really don't have any idea?"
An Energy and Commerce Committee spokesman said "the alternatives and timing" for committee action on healthcare "are dependent on the court's ruling."
"The committee's goal is to use the next few months exploring the various options," the spokesman said.