WASHINGTON (Reuters) - President Barack Obama said on Friday he will promote budget director Sylvia Mathews Burwell to be his next health secretary, who will preside over the next difficult phase of his healthcare law in the months before November congressional elections.

Burwell, whose nomination must be approved by the U.S. Senate, will replace Kathleen Sebelius, who became the public face of the disastrous rollout of Obamacare, formally known as the Affordable Care Act, which Republicans plan to exploit as they seek to take control of the Senate.

But Obama made it clear he did not blame Sebelius for the problems. In remarks interrupted multiple times by sustained cheering from White House and administration officials, he praised Sebelius, saying she will go down in history for her work implementing Obamacare.

"She's got bumps, I've got bumps, bruises," Obama said.

"Yes, we lost the first quarter of the open enrollment period with the problems with HealthCare.gov. And there were problems," he said.

"But under Kathleen's leadership, her team at HHS turned the corner, got it fixed, got the job done, and the final score speaks for itself," he said, noting that 7.5 million people have signed up for health insurance under the program, exceeding expectations.

Obama praised Burwell for her management skills and her help guiding the administration through a 16-day government shutdown last fall.

"Sylvia was a rock, a steady hand on the wheel who helped navigate the country through a very challenging time," he said.

Sebelius chuckled throughout Obama's speech, and then gave her critics some fodder by declaring there was a glitch in her speech.

"Unfortunately, a page is missing," she said.

Michelle Obama Barack obama