A majority of Americans – 52 percent – believe the health care law needs either a major overhaul or to be completely eliminated, a new NBC News/Wall Street Journal poll finds.

Forty-four percent think it either needs minor modifications or that it’s working well as is.

The Obama administration maintains that the health insurance exchange website can be fixed, but acknowledges major problems.

“In these early weeks, access to Healthcare.gov has been a miserably frustrating experience for way too many Americans,” Health and Human Services Secretary Kathleen Sebelius said Wednesday in testimony on Capitol Hill.

Read the full poll here (.pdf)

President Barack Obama addresses the issues facing healthcare.gov Wednesday during a speech at Boston's Faneuil Hall.

The number of respondents who said the law was a good or bad idea was relatively unchanged from earlier this month. But support for the law has slipped with one key group – women, who traditionally rank health care as a higher priority than men, and who are seen as an important plank in selling the law.

Americans called it a bad idea by a 47-37 percent margin – a shift from 43-38 percent earlier this month. But among women, a group President Barack Obama won by 11 points in 2012, just 38 percent think it’s a good idea, while 45 percent do not. That’s down from early October, when most women said the law was a good idea by a 41-39 percent margin.

Among white women, results are even worse. Three weeks ago, they thought it was a bad idea by a 46-36 percent margin. Now a majority say so, at 52-32 percent.

“It’s not a just a public-policy issue; it’s personal,” said Republican pollster Bill McInturff, who conducted the poll with Democratic pollster Peter D. Hart. “It has a resonance and salience that is quite different.”

He added, “It’s a reminder of the very large volume of positive information that would be required to shift these views.”

Opposition to the law has also deepened, with 43 percent “strongly” believing it is a bad idea, up 5 points from earlier this month and tied for the worst score in the poll. But that doesn’t mean all good news for congressional Republicans looking to defund or eliminate the law.

Read the full poll here (.pdf)

Only a quarter of Americans – 24 percent – said the law should be completely eliminated, including just 58 percent of Tea Party supporters, less than half of Republicans (48 percent) and just 23 percent of independents, calling into question congressional Republicans’ strategy of seeking to defund or repeal the Affordable Care Act.

The website’s woes have also not changed many minds – 50 percent said what they have heard over the last few weeks did not make them either more or less confident in the law. Forty percent said less confident, but four in five of those were already opposed to the law. Nine percent said it makes them more confident.

By a 37-31 percent margin, respondents said they think the issues with Healthcare.gov are short-term technical issues that can be corrected. Another 30 percent said it was too soon to say.

Since Oct. 1, when Healthcare.gov was supposed to be ready, Americans have been treated to a wide menu of bad news about the law. And Americans have been paying close attention.

A remarkable 83 percent said they have seen or read at least some of the news coverage about problems people have reported with the site.

To put that in perspective – that is the third-highest percentage recorded for any news story tested in the poll during the Obama presidency, behind the Trayvon Martin shooting and the 2009 town hall protests against the health care law.

Nearly six-in-10 said they have seen or read a lot about it.

That raises the stakes for the outcome of the law and Obama’s legacy, given the law is the president’s signature legislative achievement.

That means the president, whose approval rating hit an all-time low in this poll of 42 percent, missed a big opportunity to prove the law can work.

“The true damage of the rollout is this was supposed to be a period where the law would gain acceptance, and it has not,” Hart said.