President Trump decided to delay the executive order after Sen. Tom Cotton, R-Ark., pushed for the inclusion of the individual mandate repeal in the tax bill, and has been supportive of its inclusion in statements he has made on Twitter.

After initially declining to comment on the senator's statements, a White House official pushed back on the claims, saying the administration's position is that Congress should resolve the issue.

"Pursuant to the President's January EO on Obamacare, we are always looking for ways to provide relief from Obamacare," the White House official said. "The long-standing issues with the mandate would be best resolved legislatively."

The senator had told the Washington Examiner that an executive order was sitting with the Office of Management and Budget waiting for approval, but an official from the agency denied it.

"There is no EO on the individual mandate at OMB," the official said.