Sen. Lamar Alexander (R-Tenn.) on Thursday outlined an ambitious Republican agenda for fixing up Obamacare, the controversial law he called an “historic mistake.”

Alexander, the top Republican on the Senate Health Committee, spoke in a hearing to consider the nomination of Sylvia Burwell to be the next secretary of Health and Human Services. While Democrats have argued the debate over repealing the law is “over,” Alexander attacked it as a failure at the Burwell hearing, and said it has proven as disastrous as many Republicans predicted.

Lamar Alexander Tom Harkin Sylvia Burwell

Director of the White House Office of Management and Budget Sylvia Mathews Burwell greets ranking member Sen. Lamar Alexander (R-Tenn.) and committee chairman Sen. Tom Harkin (D-Iowa) at her confirmation hearing before the Senate Health Committee. (Getty Images/Alex Wong)

“We want to repair the damage that Obamacare has done and prevent future damage, as responsibly and rapidly as we can. We’d like to move in a different direction to put in place proposals that would increase freedom, increase choices and lower costs,” Alexander said. ”We trust Americans to make these decisions ourselves. We believe that is the American Way.”

Alexander said the law has led to increased health care costs, higher premiums and fewer choices, including choices about which doctor people see. He also said new insurance standards in the law have led to millions of people losing plans they liked, despite President Barack Obama’s promise that people could keep their plan if they “like it.”

“At least 2.6 million Americans have had their individual plans outlawed by Obamacare,” he said. “And millions more Americans who get their care through small businesses will find the same thing happening to them.”

Alexander also called Obamacare a job killer, and specifically noted the tax on medical device company revenue. He said this tax on revenue — which is not a tax on profits, like most taxes are — is forcing these companies to go overseas, which means lost U.S. jobs.

“The president of Costa Rica is hosting job fairs welcoming medical device companies that have been driven out of the United States by the onerous 2.3 percent tax on revenues,” he said.

Alexander said Republicans would keep pushing for changes to the law, and want to let people keep their plans, buy insurance across state lines, and provide rewards for people with healthy lifestyles. He also said Republicans would try to avoid “comprehensive” solutions because Washington isn’t smart enough to devise one.

He recounted a 2010 hearing on health care in which Republicans said Congress should take an incremental approach.

“Our Democratic friends said, that’s not a plan, that’s not comprehensive,” he said. ”We said, you’re right. Washington’s not wise enough to make these decisions to rewrite 20 percent of the economy.”

Alexander noted predictions that Republicans could take over the Senate later this year, in which case a GOP-dominated Congress could pursue a repeal of the law. Alexander did not specifically talk about this possibility, but encouraged Burwell to work with Republicans on his other piecemeal ideas for dealing with the problem of rising healthcare costs.

“Since Obama still will be in office for the next two years, if you are confirmed, we will need your help to do that,” he said.

Sen. Tom Harkin (D-Iowa), who chairs the Senate Health Committee, used his opening statement to praise Obamacare for generating more than 8 million enrollees as of early April.

While today’s hearing was held in the Health Committee, the Senate Finance Committee will be the one to confirm Burwell.