Poll: Most voters disapprove of Obama on healthcare

Among voters, 45 percent agreed with the court's ruling, while 44 percent disagreed.

Forty-seven percent, meanwhile, support the law itself and 47 percent oppose it, according to the poll.

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This division matches the one between Obama and his GOP rival, Mitt Romney, who appear to be neck-and-neck in their race for the White House. Each garnered the support of 47 percent of registered voters, with the rest giving no opinion.

At the same time, a strong majority — 58 percent — guessed that Obama will win the presidential race in 2012. Thirty-three percent, meanwhile, said Romney will win.

Voters were also split on which candidate is more trustworthy on health policy, with 48 percent favoring Obama and 44 percent favoring Romney.

Overall, the figures suggest that healthcare will loom large in voters' minds as they decide who to support for president, but not necessarily as they choose who support for Congress.

A full 77 percent of registered voters said healthcare will be an "extremely" or "very" important issue as they choose who should be in the White House. But for congressional races, a plurality of voters, 37 percent, said the issue wouldn't make much of a difference on who they would support.

Thirty-one percent said a lawmaker's support for healthcare reform would make them more likely to oppose him or her, while 30 percent said it would make their support more likely.