President Obama's approval rating and support for his signature health care law have dropped to new lows in yet another poll, which also finds the public skeptical of the administration's efforts to fix the botched Obamacare website.

A CBS News poll released on Wednesday finds Obama at a 37 percent approval rating, down 9 points from 46 percent last month. Fifty-seven percent now disapprove of the president's performance, a new high for him in CBS' polls.

The poll is just the latest to show a sharp slide in the president's numbers as the administration struggles with the Obamacare rollout.

The website to register consumers in new health exchanges continues to be plagued by technical problems as the administration's self-imposed Nov. 30 deadline for fixing nears.

Respondents believe Obama’s vow to fix problems with before December will fall short, with 64 percent not confident the website will function properly by next month and 34 percent confident.

The poll finds that 67 percent say signing up for new Obamacare insurance exchanges is not going well with 11 percent saying the enrollment process is fine.

Obama has also been forced to apologize for his broken promise that consumers could keep their current health plans under Obamacare, as insurers begin canceling coverage for millions of Americans whose policies don’t meet the law’s requirements.

Those problems have also undercut support for the law, with only 31 percent now approving of the Affordable Care Act. That number, the lowest in CBS’s polling, is down 12 points from last month. Sixty-one percent, a new high, disapprove of the law.

Only 7 percent say the health care law is working fine, with 48 percent calling for some changes and 43 percent for repealing the entire law.

Obama’s personal approval rating is also underwater at a 37-57 negative split. A slim plurality say Obama is honest at 49 percent, with 48 percent saying he is not trustworthy.

The poll was conducted from Nov. 15 to 18 and has a 3-point margin of error.