The president defended his health care law at the White House Thursday, the day after House Republicans voted again to repeal it. (The Washington Post)

Transforming the nation’s health-care system stands as Barack Obama’s most crucial piece of unfinished business, with much of his presidential legacy riding on whether it is deemed to have succeeded or failed.

While other presidents have managed to overcome intense opposition to major new social initiatives, Obama faces a degree of difficulty with health care that has no historic parallel.

So there was a certain urgency in the speech that Obama gave Thursday, the morning after the Republican-led House voted for the 38th and 39th times to dismantle all or part of the Affordable Care Act.

“There are still a lot of folks — in this town, at least — who are rooting for this law to fail. Some of them seem to think this law is about me. It’s not,” he said.

The process of implementing the law promises to be “many orders of magnitude more complicated” than establishing such programs as Social Security and Medicare, said David Blumenthal, president of the Commonwealth Fund, an organization that produces research on health and public policy issues.

Blumenthal, the Obama administration’s former coordinator of health information technology, also wrote a book on how 20th century presidents dealt with health-care policy.

He noted that both Social Security and Medicare are national programs that basically consist of paying bills and making payments to those who are eligible.

The new health-care law seeks to establish new health-insurance marketplaces and transform how care is delivered, while giving states more leeway in determining how that will be done.

Obama must also implement the new law against a united opposition party that is determined to throw as many obstacles as it can in his path.

“Obamacare is a disaster,” Sen. Marco Rubio (R-Fla.) said in a speech on the Senate floor shortly after the president’s remarks. “Mr. President, the plan is already failing.”

Some Republican lawmakers, who routinely help their constituents with concerns about Social Security and Medicare, have even served notice that they do not plan to assist those who come to them for aid in navigating the new health-care system.

“All we can do is pass them back to the Obama administration. The ball’s in their court. They’re responsible for it,” Rep. Jason Chaffetz (R-Utah) told the Hill newspaper last month.

The question of who is to blame for the fact that the bill passed without a single Republican vote is likely to remain a matter of dispute between the parties for years to come.

If the president ever had any real hope that Republicans would embrace the new law after the Supreme Court upheld its constitutionality and he won reelection, he has since given that up.

But current and former administration officials say Obama and his team have been surprised at how steadfast the opposition has remained.

“It used to be that you had a fight, and it was over, and you moved on,” said Massachusetts Institute of Technology economist Jonathan Gruber, who consulted with the administration and congressional Democrats in putting together the law.

The drumbeat of House votes against the law is little more than political theater, but the decision by nearly half the nation’s states to reject federal money to expand their Medicaid programs — a crucial element of achieving near-universal health coverage — has the potential to be far more damaging.

In some states, nearly everyone will have some kind of health coverage under the new law.

In others, a perverse result is likely: Many people who earn up to the poverty level will remain uninsured, while those who make more will receive government subsidies to purchase policies in the newly established marketplaces known as exchanges.

Administration officials say that as the benefits of the new law become more apparent, opposing it will become more difficult for Republicans.

They note that the Democrats went through much the same evolution before and after the establishment of the Medicare prescription drug program in 2003 under President George W. Bush.

After initially denouncing the drug program and vowing to repeal it, Democratic lawmakers ultimately embraced it, and even devoted town hall meetings to helping constituents sign up for it.

“We know the American people think the bill should be implemented, and if there are problems along the way, we need to address them,” said White House communications director Jennifer Palmieri. “Our goal is to implement it well. We do think the further along we get, as people get more and more benefits, the less attractive it should be for people to fight it.”

But some of those who support the new system say that will not happen without a big push from the president himself. Thursday’s event at the White House, for instance, highlighted an often-overlooked aspect of the law that has already taken effect: its requirement that insurance companies spend 80 percent of the premiums they receive on providing health care, rather than taking the payments as profit or using them to pay for overhead.

”If he had one shortcoming during the passage of the law, it was failing to be out there personally as much as he should have been,” Blumenthal said. “His legacy is on the line, and there is probably no point in holding any of his political capital back. He is all-in for making this work.”