President Obama and his daughter Malia leave Air Force One as they arrive at Andrews Air Force Base in Maryland on Sunday after their annual family vacation in Hawaii. (Carolyn Kaster/AP)

Here’s a surprisingly complex question: Can President Obama recover, politically speaking? And if so, what would that recovery look like?

The president is mired in the worst extended polling dip of his five years in office, dragged down by a series of scandals (National Security Agency spying, IRS targeting) and fumbles (the rollout of

Gallup’s month-by-month breakdown of Obama’s 2013 job-approval numbers shows a steady decline, from 52 percent in January to 41 percent by December. The Washington Post-ABC News poll pegged Obama’s job-approval rating at 55 percent in January 2013; he ended the year with just 43 percent of Americans approving of the job he was doing as president.

Obama is now far closer to the approval trajectory of George W. Bush during his second term than that of Bill Clinton or Ronald Reagan. Pew Research Center data show that a year into their second terms, Reagan’s approval rating stood at 62 percent, while Clinton’s was 58 percent. Obama was at 41 percent as of November 2013, more on par with Bush’s 36 percent in November 2005.

“I don’t think it’s possible to get to Reagan or Clinton levels from where Obama is now, especially since there are more problems looming for Obamacare,” said Glen Bolger, a partner at the Republican polling firm Public Opinion Strategies. “However, to get back to the low 50s, the president needs to rally with independent voters. Betting on that happening, however, is like betting on Andy Reid in the playoffs — not advisable!”

Digging into the numbers largely bears out Bolger’s assessment. The 12-point drop in Obama’s approval rating from January 2013 to December 2013 was attributable not to Republicans (17 percent approved in January, 13 percent in December) but rather to precipitous declines among independents (down 14 points) and, interestingly, Democrats (down 15 points).

The dip among Democrats explains why Obama has of late focused on economic inequality (unemployment insurance, a minimum-wage increase, etc.) in his speeches and policy proposals. Those moves are aimed at rallying the party’s base and, with it, Obama’s approval numbers.

But his standing among independents and Republicans speaks to the broader difficulties for the president in rebounding to Clinton or Reagan territory in his second term.

Among Republicans, Obama’s disastrous year had remarkably little impact on how they regarded him. (The decline from 17 percent approval to 13 percent was statistically insignificant.) Given that, it’s reasonable to conclude that nothing will move the president’s number among Republicans — in much the same way that, by this time in Bush’s second term, he had lost Democrats completely. If one in five (or fewer) self-identified Republicans approves of the job Obama is doing, it’s virtually impossible for his numbers to ever come close to the Clinton-Reagan range.

Then there is the independent problem. There’s little doubt that the debacle that was the rollout of the health-care Web site — and the resultant negative news coverage — damaged Obama among unaffiliated voters.

“The president is being weighed down by one issue, his health-care law,” Democratic pollster Fred Yang told the Wall Street Journal. “It’s probably fair to say that as goes health care, so goes the Obama presidency for the next year.”

The issue for Obama in Yang’s statement is that opinions about the health-care law have remained remarkably stable (and negative) for the past several years. With a single exception in September 2012, support for the law has been in the low-40s-to-high-30s percentage range since the summer of 2010, according to monthly tracking polls conducted by the Kaiser Family Foundation. That consistency suggests that changing the opinion of independents (or anyone else) on the law is an extremely difficult task.

(Worth noting: Many Democrats argue that “independent” voters are increasingly Republicans, as GOPers disaffected with the tea party wing move to the unaffiliated ranks, skewing what “independent” numbers really mean. That said, among “pure” independents, who lean toward neither party, just 25 percent had a favorable view of the health-care law in the December Kaiser tracking poll, while 52 percent had an unfavorable opinion.)

Add it all up, and you can conclude two things: 1) Obama’s best (only?) strategy to move the needle on his approval numbers in the near term is to rally Democrats, and 2) even if that happens, he will still find himself well short of the lofty ratings enjoyed by Reagan and Clinton in their second terms.

In the longer term, Republican pollster Jon Lerner argues, the best chance for an Obama approval surge is actually a GOP victory. “It will only happen if the Republicans take over the Senate in 2014 and Obama moves to the center in 2015-16, including accepting some changes to Obamacare,” Lerner argued. “In his second term, Clinton made deals with the GOP-controlled Congress. In his second term, Reagan made deals with Gorbachev.”