The basic measurement of a president’s popularity we are all used to examining is the job approval rating. By that yardstick, Barack Obama has hit a very rough patch of late; last week he registered his first sub-40% rating in the daily Gallup tracking poll of presidential job approval.
But as Reid Wilson points out in an important National Journal article, an equally important index is the president’s personal favorability, separated from specific questions of job performance. And so far, Obama has done much better on that scale:

Polling consistently shows that the majority of Americans view Obama favorably, even while they increasingly disagree with his job performance. There is a nuance to voter sentiment, pollsters say, one that provides Obama with a path to reelection. But the disconnect between the two numbers, if it ever shrinks, could also become a leading indicator that the president’s chances for a second term are headed south.

Wilson cites Bill Clinton as a president whose relatively high personal favorability ratings during his first term showed a resilience that was eventually reflected in job approval ratings and then re-election:

[I]n 1994, Clinton’s approval rating dropped to a low of 38 percent, as measured by the Pew Research Center. Clinton endured a period, from March 1994 to October 1995, during which his approval rating hit 50 percent only once. And yet, during that same period, his favorability rating stayed strong, starting around 58 percent and ending, after only a single dip below the 50 percent mark, at 56 percent in January 1996. Beginning with that January poll, Clinton’s approval rating rebounded; by November, when he asked voters for a second term, his job-approval rate stood at 57 percent.

But during his second term, George W. Bush provided an example of a president whose poor job performance assessments eroded his personal favorability, and once that happened, he never really recovered:

A July 2005 Pew survey showed 51 percent of Americans had a favorable impression of the president. By late October, that number had sunk to 46 percent, then stayed in the high 30s for most of the rest of his term. Voters had had enough; Bush’s job-approval rating led the way down, and once the favorable ratings followed, there was no way to recover politically.

So which dynamic is more relevant to Obama’s situation today? It’s hard to say for sure. Pollsters do not measure personal favorability as often as job performance. As you can see from PollingReport, the last national surveys testing Obama’s general favorability were in June, when he came in at 50% or more in polls taken by McClatchey-Marist and AP-GfK. That, however, was after Obama’s job approval rating temporarily shot up in the wake of the killing of Osama bin Laden, so perhaps it’s more relevant that polls in April and May from ABC, NBC and Fox also showed a majority smiling upon Obama personally.
As Wilson notes, the very latest measurement of favorability (though done in slightly different terms from the standard polls) is GQRR/Democracy Corps’ early August survey showing “warm” feelings towards Obama holding up despite a plunge in favorable feelings towards both Democrats and (especially) Republicans in Congress.
This data point indicates that Obama’s efforts to benefit in a bad economic and political context from comparisons to the opposition are still alive and well. And 2012 general election horse-race polling, showing Obama still typically running ahead of all named Republican presidential candidates despite flagging job approval ratings, point in the same direction. It’s worth noting that Bill Clinton’s personal popularity in his first term also benefited by comparison to an unpopular Republican Party and Republican politicians.
So it’s likely Obama still has a personal favorability cushion that could sustain him through tough sledding going into 2012. But it’s a thin cushion that could use some bolstering via improved real-life conditions and/or demonstrations of presidential leadership.