Office of Management and Budget Director Mick Mulvaney warned Wednesday that Republicans will be hurt politically if they fail to get anywhere on their promise to repeal and replace Obamacare, and said the Senate needs to try again as soon as it can.

"I don't know how you run saying something for seven years that we'll repeal and replace Obamacare if you give us the House, if you give us the Senate, if you give us the White House," Mulvaney said on Fox News. "And then when the voters give that to you, you don't follow through on that promise."

"That's the type of mistake that really follows through to haunt you in the future if you don't fix it," he said. "So I do think it's important to continue to work on healthcare."

The Senate failed by a single vote to advance a bill last week that could have become a vehicle to repeal parts of Obamacare, and it's not clear whether the Senate will try again. But Mulvaney said the White House will keep pushing for action.

"We are trying to follow through on the promises that we made as a party, which is repeal and replace," he said on CNN.

"Our point is this: Let's not move on from healthcare just because you failed by one vote," he said. "The president isn't giving up on healthcare, neither should the Senate."