Independents' job approval for Obama dropped to 36 percent in a Dec. 5-8 Pew poll, from 53 percent a year ago. Only 35 percent agreed that Obama is "able to get things done" in the December poll compared with 51 percent who said so in a January Pew poll.
Another explanation for Obama's decline has been his loss of support among Hispanics, a core component of his electoral coalition, as hopes faded for a new immigration law.
Obama's job approval among Hispanics plummeted to 48 percent in the Gallup Poll for the week ended Dec. 15 compared with 70 percent a year ago.
Public perception of the health-care law is more encouraging for the White House, Dimock said. The website failures at the start haven't done lasting damage to views of Obamacare and opinions may improve once people begin coverage, he said.
The portion of the public who said the impact of the law in coming years would be "mostly positive" rose to 39 percent in December from 35 percent in September, the Pew poll showed.
More than 1 million people have enrolled in private health insurance through government health exchanges, with more than half signing up in the first three weeks of this month, Obama said at his news conference.
While Obama's job approval remains low by the standards of his presidency, it has been edging up since early November, when he was burdened by the defective health-care website.
His 42 percent job approval in the weekly Gallup Poll ending Dec. 15 is up from a low of 40 percent for the week ended Nov. 24. That matched an all-time low for the Obama presidency set during several weeks in August and September 2011 immediately after that year's debt-limit fight brought the nation to the brink of default.
"There's no way to know whether it's the beginning of a recovery in public approval or a short-term blip," Dimock said. "But public views of the health-care law and the economy will probably determine that."