A new poll finds support for Obamacare slumping to an all-time low as the administration hits its deadline to register consumers for coverage on Jan. 1.

According to a CNN/ORC International survey released Monday, 35 percent say they support President Obama's signature domestic achievement, a drop of 5 points in under a month. Nearly two-thirds, at 62 percent, say they oppose the health law, a rise of 4 points since November.

The findings come on the Dec. 23 deadline for consumers to register in the law's new insurance exchanges if they hope to receive coverage beginning on Jan. 1, 2014.

The White House has launched a campaign to bolster enrollment in the insurance exchanges, following the rocky rollout of the healthcare.gov website in October.

The flawed website forced the administration to announce a number of delays and pressure insurers to extend the deadline to receive premium payments. But despite those efforts, the administration faces an uphill climb to reach their enrollment targets and many insurers warn that continued back-end problems with healthcare.gov could prevent many who enrolled from receiving coverage on time.

The glitch-ridden website and Obama's broken vow that consumers' could keep their current insurance plans despite new health care regulations have undercut support for the law and dramatically hurt the president in the polls. Obama has hit new lows in approval rating and measures of trustworthiness.

The push to boost low enrollment figures has targeted young people and women, but the new CNN poll finds that more women now oppose the health care law. Sixty percent of women have a negative view of Obamacare, up from 54 percent in November.

The administration has also touted the financial benefits of the law, arguing that it will save consumers. But Republicans have pounced on cases of “rate shock” to highlight many who will be hit with higher premiums under Obamacare.

The survey finds that 63 percent believe the law will cost them more for their health care, with just 7 percent saying the amount they pay for medical care will drop. Nearly 3 in 10 say it will not change.

Overall, 42 percent say they will be personally worse off and 16 percent say they will be better off under Obamacare. Forty percent say the law will have no effect.

But most believe they will be able to continue to keep the doctors they have now, another key promise made by the president as he touted the law’s benefits. Sixty-one percent say they will be able to continue to see their physicians, while 35 percent fear they will lose their doctors.

Obama though has acknowledged the problems with the website and apologized to those Americans whose current plans are being cancelled by insurers. But the president says that as more Americans begin to gain from the health care law, support will grow.

The poll was conducted from Dec. 16 to 19 and has a 3 point margin of error.