A federal appeals court in New Orleans is weighing whether to continue blocking enforcement of a judge's ruling limiting coverage requirements under former President Barack Obama’s signature health care law.

The Supreme Court’s latest rejection of a Republican effort to dismantle “Obamacare” is another sign that the GOP must look beyond repealing that law if it wants to hone the nation’s health care problems into a winning political issue.

Though increasingly conservative in makeup, the Supreme Court rejected the latest major Republican-led effort to kill the national health care law known as “Obamacare” on Thursday, preserving insurance coverage for millions of Americans.