Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellSenators introduce bill to overhaul sexual harassment policy The Hill's Morning Report — Sponsored by PhRMA — Republicans see some daylight in midterm polling Exclusive: Bannon says Rosenstein could be fired 'very shortly' MORE (R-Ky.) on Thursday said he was voting against President Obama's nominee for secretary of Health and Human Services due to her "embrace" of the healthcare law.

Sylvia BurwellSylvia Mary Mathews BurwellPrice was a disaster for HHS — Time for an administrator, not an ideologue Overnight Healthcare: GOP chairman to introduce pre-existing condition bill ObamaCare enrollment hits 11.5M for 2017 MORE is a smart and skilled public servant. But her embrace of ObamaCare calls her policy judgment into question,” McConnell said on the Senate floor. “And when it comes to the task of implementing this ill-conceived and disastrous law, the president may as well have nominated Sisyphus. Because, as I indicated, Ms. Burwell is being asked to do the impossible here.”

Later Thursday, the Senate confirmed Burwell to replace outgoing HHS Secretary Kathleen Sebelius in a 78-17 vote. More than 20 Republicans joined Democrats in voting for her, while others in the GOP, such as McConnell, voted no.

Burwell’s major task will be the implementation of the healthcare law — an effort that McConnell said is doomed to failure.

“The Senate will vote on President Obama’s newest choice to head the Department of Health and Human Services. In other words, the person he’ll be sticking with the impossible task of trying to make ObamaCare work,” McConnell said. “In my view, the Senate shouldn’t be focusing on a new captain for the Titanic. It should focus on steering away from the iceberg.”

On Wednesday, the Senate easily advanced Burwell’s nomination in a 67-28 vote, with 14 Republicans joining Democrats to end debate.

Burwell was unanimously confirmed to her current role as director of the Office of Management and Budget.

But some Republicans have said they'd still oppose her nomination as a protest against ObamaCare.

“She’ll be the Chief Operating Officer of ObamaCare implementation — a law that’s doing incredible damage to middle-class families in this country,” McConnell said. “And her embrace of this disastrous law is reason enough to oppose her confirmation.”

McConnell is facing a tough reelection race in November and has been an ardent critic of ObamaCare.

— Ferdous Al-Faruque contributed to this article.

This story was first posted at 10:42 a.m. and has been updated.