Memphis Mayor A C Wharton encourages residents of his city to sign up for the Affordable Care Act during a rally Monday. The new health insurance marketplaces will open Tuesday. (Jim Weber/Commercial Appeal via AP)

As most of Washington comes to a halt, President Obama is betting that Tuesday will be remembered in history for what he believes cannot be stopped.

“The Affordable Care Act is moving forward. That funding is already in place. You can’t shut it down,” Obama warned Republicans as the final hours before the shutdown deadline ticked away.

The day has arrived when millions of uninsured Americans have their first chance to sign up for what the administration says will be high-quality, affordable health coverage. That achievement is something presidents of both parties sought unsuccessfully for more than 60 years.

The coming months and years will show whether the new health-care law, commonly known as Obama­care, lives up to its aspirations. Those who sign up now, for instance, will not begin to receive benefits until January.

It faces challenges that are both substantive and political, and a degree of difficulty that has no historical parallel.

Wonkblog's Sarah Kliff breaks down the policy you need to understand about the Affordable Care Act, from politics to premiums. (Kate M. Tobey/(In Play))

Social Security and Medicare look almost simple compared with the system that will be put into place with the Affordable Care Act. Obamacare seeks to establish new health insurance marketplaces and transform how care is delivered, while giving states significant leeway in determining how that will be done.

Not only must the complicated operation work as Obama has said it will, but it must survive a continued assault by Republicans, who demanded repeal or delay of the law as the price of keeping the government open and the nation solvent.

They also are certain to seize on every technical glitch and misstep.

“I’ve never seen a law implemented with so many delays, mistakes and problems,” House Small Business Committee Chairman Sam Graves (R-Mo.) said last week after the administration announced that online enrollment in the new marketplaces for small businesses would not proceed on schedule.

The Treasury Department has also delayed by a year the requirement that businesses with 50 or more full-time employees provide coverage for their workers or face a fine — a move that the administration said was proof of its flexibility but one that opponents contended was an early warning of disaster.

Implementing a big new law “is not sexy. It’s not exciting. But it’s critically important, and it’s incredibly hard,” said Gautam Mukunda, author of the book “Indispensable: When Leaders Really Matter.”

In the case of the Affordable Care Act, implementation is made all the more difficult by how many moving parts are outside the president’s reach.

“He has significant but not total control over the federal bureaus; he has no control whatsoever over the states,” said Mukunda, who teaches at Harvard Business School. “But he’s going to get the blame for anything that goes wrong.”

It also remains to be seen whether Obama — who has often expressed frustration at his inability to explain the law in a compelling way — can muster the kind of leadership it will take to win over a skeptical public.

“The president has to continue to focus,” said Robert J. Blendon, a professor of health policy and political analysis at Harvard University. He added that the launch of the new health-care system “is a historic evolution of events. It is not a day.”

Finding a way to provide medical coverage for all has eluded presidents at least as far back as Harry S. Truman.

“What did the Republicans do with my proposal for health insurance? You can guess that one. They did nothing,” Truman said during his grueling whistle-stop campaign in 1948. “Does cancer care about political parties? Does infantile paralysis concern itself with income?”

Initially, at least, Obamacare will fall well short of universal coverage. That is because, when the Supreme Court upheld the law’s constitutionality last year, it struck down the part that required states to expand their Medicaid programs to include everyone below the poverty line.

About 6.4 million poor people will be left behind because they live in states that either have chosen not to broaden eligibility for their Medicaid programs or have not made a decision, according to a recent analysis by the Henry J. Kaiser Family Foundation.

Nonetheless, the health-care act marks the most ambitious new social program since 1965, when President Lyndon B. Johnson signed the law that established Medicare for the elderly and Medicaid for the poor.

As hard as it had been to get that law passed against opponents as powerful as the American Medical Association, which had warned that Medicare would be “the beginning of socialized medicine,” Johnson knew that was just the beginning.

“Perhaps never — except in mobilizing for war — has this government made such extensive preparations for any undertaking,” LBJ wrote in a telegram to the AMA a week before the new programs launched.

Johnson had an additional concern: Medicare and Medicaid were put into place shortly after the Civil Rights Act of 1964, and he saw them as levers to force Southern hospitals to integrate.

“He personally kept track of every hospital in the South, and for the ones that were not complying, he called their governors,” said David Blumenthal, president of the Commonwealth Fund, a national philanthropy that researches health and social policy issues.

Harvard’s Blendon noted that Obamacare would not be the first major health initiative to get off to a slow and bumpy start. It took 17 years before Medicaid was adopted in all 50 states, with Arizona being the last to accept it.

But a rocky launch can also doom a health initiative, as happened in 1988, when President Ronald Reagan signed a law that imposed a Medicare surtax to pay for coverage of catastrophic medical expenses and prescription drugs.

After a mob of livid elderly people chased House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) down a Chicago boulevard and then surrounded his car, Congress got the message and repealed the law.

Prescription drug coverage was revived in 2003, when it was passed by a Republican Congress and signed by President George W. Bush.

The 2014 midterm elections loom as an important political test for Obamacare.

If Democrats do well and hang on to the Senate, opponents may begin to accept the law as a fait accompli, and recalcitrant states may find it more politically palatable to accept federal money to expand their Medicaid programs.

Obama health-care adviser Chris Jennings argued that Americans will warm up to the law when they begin to experience its benefits.

“They need to see how it is working for them,” he said.

That is only the first step on what could be a long road to public acceptance.

Ultimately, Blendon said, “the power of the law will be the voices of people who have health insurance who didn’t before. If you give coverage to people, it is going to be hard to ever take that coverage away.”

Brady Dennis contributed to this report.