No matter his policies or job performance, a majority of Americans have always trusted President Obama. That has now changed. (The Washington Post)

Essential elements of Brand Obama in 2008 were trustworthiness and competence, virtues the candidate used to contrast himself with his predecessor, George W. Bush.

Obama promised honesty in foreign policy — no unfounded claims of weapons of mass destruction to justify a military invasion. He pledged precision in governing — no Hurricane Katrinas.

And he vowed to be forthright with the American public and U.S. allies when it came to post-Sept. 11 counterterrorism policies, shadowed by the legacy of torture, black-site prisons and the National Security Agency’s warrantless wiretapping.

The emphasis on good government helped him win his first and second presidential elections and to bounce back from periods when his overall approval rating was scraping lows. People liked him, even if they didn’t like his politics, as an earnest leader who made a priority of having dinner each evening with his young family.

But his likability among the general public has fallen sharply in recent weeks amid the self-inflicted problems with implementation of his health-care law.

A new Quinnipiac University poll this week found for the first time that a majority of Americans — 52 percent — say Obama is not honest or trustworthy. A Gallup poll released Wednesday showed a five-percentage-point drop since September on those same issues and a 10-point fall since the middle of last year.

Now, according to Gallup, only half the country thinks Obama is honest.

The pair of recent polls also showed a continuing decline in his approval rating, tracking several other national surveys that have the president near new lows in overall popularity. But Obama has rebounded from such dips before, in part because much of the country still liked him personally and trusted him politically.

That political cushion has virtually disappeared, with his marks on honesty only slightly better than his poor approval rating.

The plummet in public confidence in Obama’s character poses a much larger problem for his governing agenda and for his legacy than general approval ratings. The erosion comes primarily from independent voters and from his own base, crucial to his party’s success in next year’s midterm elections.

The impact of the slide could be wide-ranging. His pursuit of a deal to curb Iran’s nuclear program, for example, may be more difficult to sell to a less-trusting public, especially given strong resistance in Congress and in Israel.

Second-term trust problems

Many second-term presidents run into trust problems, but in important ways the problem Obama now faces is more pressing. Honesty goes to the rationale for his election and to the core of his philosophy that government is something to be trusted, not feared or ridiculed as his political opponents claim.

President Obama's job approval ratings have declined.

Bill Clinton had the Monica Lewinsky affair shape his second term. But Clinton had to overcome questions about his fidelity during his first campaign and never made trust a central issue. A vote for Clinton came with a “buyer beware” clause that Obama never needed.

Ronald Reagan ran into trouble for the Iran-contra scandal — missile sales to Iran to illegally fund the armed opposition to Nicaragua’s Sandinista government. But Reagan was an avowed anti-communist, and, while damaged by Iran-contra, his popularity rebounded late in his term.

George W. Bush promised a cleaner government than Clinton’s and a “compassionate conservatism” in domestic politics, until the Sept. 11, 2001, terrorist attacks changed his presidency into a more ideological administration. But it was Bush’s weakness in management — of postwar Iraq and of the emergency response to Katrina — that permanently harmed his presidency and shaped the candidacy of his successor.

Obama’s problems now are more urgent because they have come so early in his second term, with few obvious opportunities to repair his image.

His early first-term moves to rescue the auto industry, bail out an insurance giant and pass an enormous mix of spending increases and tax cuts angered conservative critics but won popular support for stabilizing a fast-falling economy. At the end of his first 100 days in office, nearly three-quarters of the electorate said he was trustworthy, according to a Washington Post-ABC News poll at the time. His approval rating was only five points lower than that.

That gap between approval and trust widened throughout his first term, giving him leeway to pursue even unpopular policies, particularly among independent voters who value competence over ideology.

After the first debt-ceiling showdown in the summer of 2011, Obama’s approval rating stood at 42 percent, according to a Quinnipiac poll at the time. But 58 percent of those same respondents said Obama was trustworthy.

Fifteen months later, after spending more than a billion dollars to polish his image and contrast himself with a Republican candidate whom he cast as untrustworthy, he won reelection.

Little to fall back on

With no election campaign ahead, Obama has fewer opportunities to focus national attention on his agenda and any fixes he has made to his administration. How he recaptures the approval of independents — who are abandoning him, according to a Pew Research Center poll last week — will be a challenge for his insular political team.

On Wednesday, the administration announced that in October, about 27,000 people were able to buy private insurance through the federal exchange, a small fraction of initial government projections.

The problem highlights Obama’s central struggle as public trust slips away. As a champion of government’s effectiveness, Obama has little to fall back on when government fails, as it has so dramatically in rolling out the health-care Web site.

The problems with the Affordable Care Act, his signature domestic policy achievement, cast serious doubt on whether he has paid proper attention to the details of governing. A commander in chief who approved the successful strike that killed Osama bin Laden is now facing a decline in public faith in his competence.

Perhaps more damaging to his credibility has been the wave of health insurance policy cancellations that have come during the health-care law’s enrollment period, leaving many Americans forced to pay more for new policies that cover a broader range of government-mandated services.

In selling the legislation, Obama promised that such changes would not take place, frequently telling audiences, “If you like your plan, you can keep your plan.” Last week, he apologized for misleading the public.

According to the new Quinnipiac poll, only 36 percent of respondents say they approve of how he has handled his signature issue.

Disclosures of the long reach of NSA eavesdropping in monitoring e-mail and tapping foreign leaders’ cellphones have also united elements of the Republican right and the Democratic left in opposition to Obama’s policies.

But that anger has not translated into a political problem for the president, at least not on the scale of the health-care problems. The Quinnipiac poll showed that 52 percent of respondents approved of his effectiveness against terrorism — the only major category in which the president received majority support.

Sean Sullivan and Scott Clement contributed to this report. Clement is a pollster with Capital Insight, the independent polling group of Washington Post Media.