Updated

President Obama is struggling to stop the steady slide in public support for his health care law, as yet another poll shows public approval of the law -- and his job performance -- hitting a new low.

The survey from CBS News depicts a startling drop in support for the Affordable Care Act. Approval dropped to 31 percent, down 12 points since October.

According to the poll, the president's approval rating also slipped to 37 percent, from 46 percent just last month.

Both figures represent the lowest of Obama's presidency in CBS polling.

While Republicans are united in their opposition to the health care law, the latest numbers reflect new skepticism among Democrats and independents.

Obama has been facing criticism from his own party for both the failures of HealthCare.gov as well as cancellation notices that have gone out to those on the individual market whose policies did not make the cut under ObamaCare's new standards. The president last week gave insurance companies a one-year extension, allowing them to re-offer those out-of-compliance plans.

But it's unclear how many insurance commissioners and companies will consent, given the difficulties of making the sudden switch after years of planning. The president plans to meet with insurance commissioners on Wednesday afternoon.

The CBS News poll followed a Washington Post-ABC poll that showed Obama's job approval rating at a meager 42 percent -- and his disapproval rating at 55 percent, the worst of his five years in office.

That figure matches the disapproval rating he received in a recent Fox News poll.

Among women, who were some of the president's core supporters during the 2012 campaign, the president is also losing traction. The Washington Post-ABC poll showed just 44 percent of women approve of the job he's doing, while 52 percent disapprove.

Amid the downturn in the numbers, Obama has tried to rally his base -- and his base has tried to rally for him. An email from MoveOn.org went out on Wednesday warning the ObamaCare problems have triggered a "Washington feeding frenzy."

"President Obama is doing all he can to save Obamacare, but he can't do it alone. He needs us to join him and fight back," the email said, appealing for money.

Speaking Wednesday at the Wall Street Journal CEO Council meeting in Washington, Obama noted that nobody in Washington is doing particularly well in the polls right now. Congress is more unpopular than the president, according to most polls.

But Obama stressed that the administration must fix the health care website, and acknowledged some concern over signing up enough people to make the new marketplaces work.

"It's something that we have to pay attention to," Obama said.

The CBS poll of 1,010 adults was conducted Nov. 15-18, and had a margin of error of 3 percentage points.