Rep. Brian Babin, Republican of Texas, has introduced a bill called the "SCOTUScare Act," which would compel the Supreme Court to be on Obamacare. The name of the act is a nod to Justice Antonin Scalia, who in a bitingly sarcastic dissent to Thursday's 6-3 decision wrote, "We should start calling this law SCOTUSCare."
"As the Supreme Court continues to ignore the letter of the law, it's important that these six individuals understand the full impact of their decisions on the American people," Babin said, according to TheHill.com.
"By eliminating their exemption from Obamacare, they will see firsthand what the American people are forced to live with," he said.
Read MoreObama: Affordable Care Act is 'here to stay'
The court's ruling Thursday, written by Chief Justice John Roberts, said that Obamacare subsidies must be available to customers of government-run insurance exchanges across the United States, regardless of whether the marketplace is being run by a state or the federal government. The subsidies are available to people with low and moderate incomes.
Plaintiffs in the case known as King v. Burwell unsuccessfully argued that customers of HealthCare.gov, the federal exchange that serves two-thirds of the U.S., were ineligible for these subsidies.