(Bloomberg) — President Barack Obama’s health care law is becoming more entrenched, with 64% of Americans now supporting it outright or backing small changes.

Even so, the fervor of the opposition shows no sign of abating, posing a challenge for Obama’s Democrats during congressional races this year, as a Republican victory in a special Florida election this week showed. In addition, 54% of Americans say they’re unhappy with the president’s handling of the issue, according to a Bloomberg National Poll.

That’s an improvement since the last poll, in December, when Obama’s public standing on health care hit a low of 60 percent disapproval after the botched rollout of the insurance exchanges, according to the March 7-10 poll of 1,001 adults.

“Things definitely seem to be getting better,” said Paul Attard, 50, a political independent in Evergreen, Colorado and a program manager for a cell-phone company who wants the law modified rather than repealed. “It seems like they are getting a lot more people to join. It’s a sign that the system is working.”

Through March 1, 4.2 million Americans had enrolled in health plans via the Affordable Care Act’s insurance exchanges, the government said this week. The deadline for enrollment is March 31, and the Congressional Budget Office has estimated that 6 million people will sign up this year for private plans.

Highest acceptance

Fifty-one percent of Americans favor retaining the ACA with “small modifications,” while 13% would leave the law intact and 34% would repeal it. That’s the highest level of public acceptance for the law yet in the Bloomberg poll.

Investors are betting the law will withstand political challenges. An “Obamacare” portfolio of stocks that benefit from the law developed by the online broker Motif Investing is up 40.9% over a year ago as of March 12, almost doubling the performance of the Standard & Poor’s 500 index, which returned 22.9%.

A “Repeal Obamacare” portfolio underperformed the benchmark stock index, rising 16.1% during the period.

The law’s opponents have the advantage of intensity, which was on display in the March 11 Florida election for a vacant congressional seat. After a campaign focused on differences over Obamacare, Republican David Jolly turned out more of his supporters than did Democratic candidate Alex Sink. The election drew little more than half as many voters in the district as in the 2012 presidential race, when Obama narrowly carried it and a since-deceased Republican congressman was re-elected.

‘Major’ decider

“In off-year elections, turnout is a huge factor,” said J. Ann Selzer, who conducted the survey for Bloomberg. “The anti-Obamacare segment is both more likely to say they will definitely vote and more likely to say their vote will be strongly influenced by their view of Obamacare; that can be enough to sway a race.”

Seventy-three percent of Bloomberg poll respondents who would repeal Obamacare say the law will be a “major” decider of their vote, compared with 45%of those who support modifications and 33% of those who back the law as is.

Repeal advocates are also the most likely to vote, with 73% saying they will “definitely” do so. By contrast, 61% of those who want only small modifications are likely voters as are 54% of those who want the law kept intact.

Alternate perceptions

Republicans and Democrats have become so polarized over the ACA they have alternative perceptions of how the law has touched their families and friends.

Fifty-nine percent of Republicans say they personally know someone who has been hurt by the law and only 14%say they know someone who has been helped. Among Democrats: 48% say they know someone the law has helped and only 19%know anyone who has been hurt.

Party identification and political ideology track responses to the question more closely than do traits such as income, education and race that usually are more closely linked to differences in health-coverage experiences.

Even with public acceptance of the law, 72% of Republicans favor repeal. That’s one reason the Republican-controlled U.S. House has voted about 50 times to repeal all or part of the law and opposition is an article of faith among the party’s presidential aspirants.

Keeping provisions

Still, rank-and-file Republicans want several key provisions retained. Sixty-two percent of Republicans want to retain the law’s ban on denying coverage based on pre-existing medical conditions, and 57% want to keep the requirement that insurance companies allow children up to age 26 to stay on their parents’ policies.

Republicans are about evenly divided on the elimination of lifetime limits on medical benefits.

Even majorities of those who would repeal the law want to maintain some of those provisions. Fifty-eight percent of repeal backers favor keeping the prohibition on denying coverage based on pre-existing conditions, and 58% also want to continue to allow those up to age 26 to remain on their parents’ policies. A substantial 40% minority of repeal advocates would keep the law’s ban on lifetime caps on insurance benefits.

Those provisions are more popular with the country as a whole. Sixty-five percent of Americans support the ban on denying coverage based on pre-existing conditions, 73% want to let children stay on policies up to age 26, and 53% favor the elimination of lifetime caps.

Unpopular mandate

A 51% to 47% majority of the country opposes the requirement that all Americans carry health insurance. Political independents oppose the mandate by 55% to 42%.

Though Obama has argued that the law gives Americans security that they’ll never go without coverage, and Republicans have warned that it will undermine the medical system, the poll doesn’t detect much movement in public anxiety over health care.

Americans’ outlook on their own health-care costs has improved modestly, though a majority remains pessimistic. Fifty-two percent say they expect medical costs to be worse in 12 months, down from 61% in December.

Two-thirds say they have seen no change in the quality of their care compared with a year ago, while 13% say they are better off and 19%worse off.

Americans are about evenly divided on whether they face a greater or lesser risk of losing access to insurance than a year ago, with 38% saying they are more worried about the possibility and 41% less worried. The remainder say the risk was about the same or were unsure.

The Bloomberg Poll, conducted by Selzer & Co. of Des Moines, Iowa, has a margin of error of plus or minus 3.1 percentage points.

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