A new poll shows support for Obamacare underwater but inching up, months after the disastrous rollout of the healthcare.gov website.

Thirty-nine percent now say they support President Obama's signature domestic achievement, up from 35 percent in December, according to a poll released Tuesday by CNN/ORC International.

But nearly two-thirds still oppose the law, with 57 percent giving it a thumbs down, a drop in 5 points from December.

The poll's findings come as the administration pushes a last-minute enrollment drive ahead of their March 31 deadline.

Four million Americans have signed up for state and federal exchanges at last count, but that figure is still behind the 7 million the administration hoped to sign up. And initial reports show a shortage of the young, healthy consumers needed to make the law work.

The poll found that most of the new support for Obamacare comes from upper-income Americans. Among people who make $50,000 or more, support grew from 36 to 46 percent. Support remained steady at 35 percent since December among those making less than $50,000.

The administration says that problems with online enrollment have now been fixed and is encouraging Americans to sign up.

But critics say that many questions remain unanswered, including what percentage of enrollees have actually paid their premiums and what number were previously uninsured.

The administration has been forced to issue a number of delays to key provisions of the law but Obama has insisted that the March 31 deadline for the individual mandate is final.

The poll was conducted from March 7 to 9 and has a 3.5 percent margin of error.