WASHINGTON (CNN) -

Support for the country's new health care law has dropped to a record low, according to a new national poll.

And a CNN/ORC International survey released Monday also indicates that most Americans predict that the Affordable Care Act will actually result in higher prices for their own medical care.

Only 35% of those questioned in the poll say they support the health care law, a 5-point drop in less than a month. Sixty-two percent say they oppose the law, up four points from November.

Nearly all of the newfound opposition is coming from women.

"Opposition to Obamacare rose six points among women, from 54% in November to 60% now, while opinion of the new law remained virtually unchanged among men," CNN Polling Director Keating Holland said. "That's bad news for an administration that is reaching out to moms across the country in an effort to make Obamacare a success."

According to the survey, 43% say they oppose the health care law because it is too liberal, with 15% saying they give the measure a thumbs down because it is not liberal enough. That means half the public either favors Obamacare, or opposes it because it's not liberal enough, down four points from last month.

Sixty-three percent say they believe the new law will increase the amount of money they personally pay for medical care, which may not be a good sign for a law known as the "Affordable Care Act."

The survey also indicates that 42% say they will be personally worse off under Obamacare, with 16% saying the law will help them, and four in 10 saying it will have no effect on them.

Just over six in 10 say they believe they will be able to receive care from the same doctors that they now use, with 35% saying they will not be able to see the same doctors.

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Poll: Health care law support hits new low