That contrasts sharply with Medicare and Social Security, which remain popular because almost everyone who benefits paid something into the system. “That was done because it sat better with the American cultural idea of self-reliance,” said David M. Kennedy, a Stanford University historian.

In addition, Republicans argued effectively that the law was changing the status quo, affecting people who already had private health insurance, said Representative David E. Price, Democrat of North Carolina.

“There was an ability to exploit the unknown, to exploit the fear of people losing something that they have,” said Mr. Price, a political scientist. “That wasn’t true with Social Security and Medicare.”

The focus on the law’s expansion of coverage for those of modest means has also overshadowed popular, more broadly enjoyed benefits like allowing parents to keep their children on their plans until they are 26 and barring insurance companies from denying coverage because of pre-existing conditions.

“This is where the communications failure has been so problematic,” said Ezekiel J. Emanuel, one of the law’s architects. “We haven’t really alerted Americans to the fact that there is much more to this than the exchanges that’s going to be really, really positive for all of us, not just those getting insurance.”

That view has not taken hold, especially among white voters who see the law as an act of government redistribution to the 15 percent of the population that is uninsured. In a New York Times/CBS News poll in December, just 17 percent of whites said the health law would help them while 41 percent said it would hurt; among blacks, 42 percent said it would help them while 15 percent predicted it would hurt. Four in 10 whites and blacks said it would have no effect on them.

This divide was easy to detect in Atlanta, where symbols of ethnic diversity abound — the city’s hip new barbecue restaurant, Sweet Auburn, is named after Atlanta’s historically black neighborhood and owned by a Chinese-American — but reminders of old divisions are just as evident.