"As public support for this law nears an all time low, it’s time for the President’s administration to realize that everyone deserves an exemption from ObamaCare — not just his Washington allies," said RNC Chairman Reince Priebus in a statement.
Chatter about ObamaCare implementation rose this week after President Obama addressed the issue in a press conference.
Obama acknowledged there would be some "glitches and bumps" in the law's rollout, but urged the average American not to worry.
"Despite all the hue and cry and sky-is-falling predictions about this stuff, the part of ObamaCare that affects you is already in place," he said.
The Affordable Care Act's major provisions — its state insurance exchanges and Medicaid expansion — take effect Jan. 1.