Public support for the Affordable Care Act narrowly notched a new high in the latest ABC News/Washington Post poll, while criticism of Barack Obama's handling of the law's rollout - although still substantial - has eased from its peak last fall.

Views hardly are enthusiastic: With the year's sign-up deadline upon us, Americans split on Obamacare, 49 percent in support, 48 percent opposed. But that compares with a 40-57 percent negative rating after the initial failure of the federal enrollment website last November.

See PDF with full results, charts and tables here.

While still shy of a majority, 49 percent support is numerically the highest on record - albeit by a single point - in more than 20 ABC/Post polls since August 2009. The previous high was 48 percent in November 2009. The low was 39 percent in April 2012; the average, 45 percent.

Taking it another way, while not statistically significant, this survey's +1 positive score for the law is a first. Other than an even 47-47 percent in July 2012, it's been numerically negative in every other measurement, ranging from -1 to last November's -17, averaging -5 points.

Most of the advance in support for the law came in December, marking November's sharply negative turn as a blip inspired by HealthCare.gov's crash landing. Most of the gains in approval of Obama's handling of the law, by contrast, occurred just in the past month.

Among groups, this poll, produced for ABC by Langer Research Associates, finds that support for Obamacare compared with last November has gained among young adults, nonwhites, lower-income adults, those who lack a college degree - and, in a surprising result, political conservatives. While just 36 percent of conservatives back the law, that's up from a mere 17 percent in the fall.

OBAMA/GOP - Obama, for his part, receives continued criticism for the law's implementation. But disapproval has backed off from 63 percent in November to 54 percent now, while approval for his work on the rollout is up by 11 points, including six points this month, to 44 percent.

Further, reflecting the public's overall division on Obamacare, there's also a split on efforts by the Republicans in Congress to replace it with a new health care law: Forty-seven percent of Americans support that move, with 49 percent opposed.

Partisanship drives that boat. Seventy-six percent of Democrats support the ACA, compared with 20 percent of Republicans. By contrast, 85 percent of Republicans support efforts to create a GOP alternative, vs. 19 percent of Democrats.

CHANGE - Views on the law, as noted, have shifted disproportionately in an unexpected area - among conservatives. While most remain opposed, that's declined from 81 percent in November to 61 percent now. Similarly, while conservatives are particularly critical of Obama's handling of the law, this has eased from 84 percent disapproval last fall to 69 percent today.

These shifts have occurred disproportionately among conservatives who are not also Republicans, as well as among those who identify themselves as "somewhat" as opposed to "very" conservative. There's been a 25-point increase in support for the law among non-Republican conservatives, vs. 8 points among conservative Republicans; and a 27-point increase among somewhat conservatives, vs. 10 points among strong conservatives.

Independents, potential swing voters in the midterm elections, continue to tilt against the law, with 44 percent in support, 54 percent opposed, but that compares with 36-62 percent last fall. And while just 37 percent of independents approve of Obama's handling of the rollout, that is 14 points more than its low four and a half months ago.

Among other groups mentioned above, support for the ACA is up by 16 points vs. November among adults under age 40 - a coveted group for the law's insurance pools - from 38 percent then to 54 percent now. It's gained a similar 15 points among those with incomes less than $50,000, from 38 percent then to 53 percent; 14 points among nonwhites, to 68 percent (compared with just 40 percent support among whites); and 12 points among those who lack a college degree, to 46 percent support.

Finally, intensity of sentiment remains more negative than positive: Thirty-six percent of Americans "strongly" oppose the law vs. 25 percent who strongly support it. But, as with other results, that's moderated, from 19 points net negative last fall to 11 points today.

METHODOLOGY - This ABC News/Washington Post poll was conducted by landline and cell phone March 26-30, 2014, in English and Spanish, among a random national sample of 1,017 adults. Results have a margin of sampling error of 3.5 points. The survey was produced for ABC News by Langer Research Associates of New York, N.Y.