WASHINGTON — President Obama took the oath of office on a bright shiny day in January, declaring that “America’s possibilities are limitless.”

Eleven tumultuous months later, Obama closes out the year after a string of political calamities – including self-inflicted wounds such as the chaotic rollout of the health care law and a questionable response to Syria – sent his job approval ratings plunging and raised questions about the administration’s competency and the president’s credibility.

Nearing five years into his presidency, America’s possibilities might well be limitless, but Obama’s are another matter.

Obama insists that 2013 wasn’t a lost year, citing an improving economy and a declining unemployment rate as important progress.

“I took this job to deliver for the American people, and I knew and will continue to know that there are going to be ups and downs on it,” Obama said Friday in his last news conference of the year. “My goal every single day is just to make sure that I can look back and say we’re delivering something, not everything, because this is a long haul.”

If he’s focused on the American people, the response might sting. A majority of voters don’t trust him or don’t have confidence in his leadership.

“Those findings are particularly worrisome for Obama,” said George Edwards, a presidential scholar at Texas A&M University. “At this point in the presidency, if people conclude the president isn’t trustworthy, they’re not likely to change their minds. If they conclude he’s not up to the job, they’re unlikely to switch.”

At the Capitol, Obama was routinely thwarted during the year. Much of his agenda did not pass, including a rewrite of U.S. immigration laws and gun control legislation. And nothing was more damaging to Obama than his administration’s inept rollout of the health care law.

The slew of problems that bedeviled his signature domestic achievement included an error-laden website that required the intervention of top-level tech experts to fix, and the revelation that Obama had not told the truth when he repeatedly promised Americans that they could keep their health care plans if they wanted.

Fresh from his re-election, Obama opened the year with an aggressive agenda: a call to overhaul the nation’s immigration laws and to tighten gun regulations, sparked by the nation’s horror after 20 children were killed at a Connecticut elementary school a month earlier.

But a resounding defeat on gun control took some of the wind out of the administration’s sails.

Despite enlisting everyone possible to help – with a push by Vice President Joe Biden and with first lady Michelle Obama making a rare foray into politics – Obama suffered a defeat in April as a divided Congress flatly rejected his call to expand background checks, renew an assault weapons ban and limit the size of ammunition clips.

The problems continued in May as the Internal Revenue Service acknowledged it had inappropriately targeted groups that had political-sounding names.

It got no better for Obama with the release in June of classified information detailing the far reaches of the surveillance programs that have guided intelligence gathering since the Sept. 11, 2001, terrorist attacks.

Documents obtained by former government contractor Edward Snowden revealed the National Security Agency had been collecting telephone and email records of Americans and foreigners, eavesdropping on allies like Germany and Brazil, and spying on global institutions, such as the World Bank.

Republicans took a beating in the polls over a 16-day federal government shutdown, which overshadowed, for a time, problems with the Oct. 1 health care rollout. But Obama was forced to scrap a trip to Asia, setting back the administration’s efforts to focus on the region.

Still, there was an upside to the wrangling: Congress last week sent Obama a rare bipartisan budget deal, breaking two years of near-constant budget brinksmanship.

In recent weeks, Obama has begun to shuffle staff in hopes of regaining momentum for his sixth year in office, which is historically a tough year for presidents to secure legislative accomplishments, given looming midterm elections.

Obama may not persuade lawmakers to pass large, politically tough bills – such as changing the tax code or overhauling entitlements – but he may find modest legislative successes, including a farm bill and confirmation of appointments, Feehery said.

Obama, though, still rates higher than members of Congress.

“He limps through the closing hours of 2013, but so do his folks across the aisle from him,” said Lee Miringoff, director of the Marist Institute for Public Opinion in New York. “This isn’t fatal.”

Some Democrats say they believe the tide is beginning to turn.

In addition to unfinished business, such as immigration, Obama signaled recently that he will push Congress to act on the income disparity between rich and poor through proposals such as jobless benefits and a higher minimum wage.

Pessimism has turned into optimism for Steven Vancore, a Democratic consultant in Florida, in part because of the recently passed bipartisan spending plan.

“This budget deal gives me a ray of optimism,” Vancore said. He noted that most of Obama’s hurdles this year were the type any president could face, but for the fumbled health care rollout. Yet, he offers with the website seemingly on its way to full operability, “I’m optimistic he could get things done.”