Obama, coming off 11 straight primary and caucus victories, had the support of 54 percent of Democratic primary voters nationally. Clinton had 38 percent support.
In a CBS News poll taken three weeks ago, shortly before Super Tuesday, Obama and Clinton were tied at 41 percent. Clinton led by 15 points nationally in January.
The former first lady has lost her advantage among women, according to the poll: The two leading Democrats now have even levels of support among female primary voters.
Men, meanwhile, disproportionately favor Obama. He leads Clinton among male Democratic primary voters 67 percent to 28 percent, and leads among white men 61 percent to 33 percent.
Fifty-nine percent of Democratic primary voters said Obama has the best chance of beating likely Republican nominee in the general election. Twenty-eight percent said Clinton is most likely to win in November.
Obama is now seen as the likely Democratic nominee: More than two-thirds of Democratic primary voters said they expect the Illinois senator to win the nomination.
When all registered voters were asked who they favored in a head-to-head general election match up between Obama and McCain, Obama led by 12 percentage points, 50 to 38 percent.
In a Clinton-McCain match up, registered voters were evenly split, with 46 percent backing each candidate.
Obama beats McCain by 10 points among independents, while McCain beats Clinton by 17 points among that group.
Democrats Say Differences Between Obama, Clinton Aren't On The Issues:
Democratic primary voters do not see significant differences among Clinton and Obama on two of the issues most important to them: Majorities of those polled see only "minor" differences between the two on the war in Iraq and health care.
But Democratic primary voters were more likely to identify Obama as someone who cares about them "a lot" (63 percent for Obama vs. 46 percent for Clinton), someone who makes them feel inspired about the future (69 percent for Obama vs. 54 percent for Clinton), someone who would compromise the right amount with Republicans to get things done (67 percent for Obama vs. 55 percent for Clinton), and someone who could bring change to Washington (70 percent for Obama vs. 60 percent for Clinton).
Bill Clinton's involvement in the race has split Democrats. The percentage of primary voters who said the former president's involvement has made them more likely to support Hillary Clinton - 22 percent - was equal to the percentage who said it made them less likely to support the former first lady. 55 percent said it made no difference.
Read The Complete CBS News Poll On The Democratic Race
The General Election
The Economy And War In Iraq
A majority of Democratic primary voters said that the superdelegates - the party insiders who could decide the nomination if the race remains tight - should back whichever candidate gets the most overall elected delegates. A quarter said they should back whomever they want, while 20 percent said they should back the candidate with the best chance to win in a general election.
Republicans Accept McCain, But Enthusiasm Lacking:
On the Republican side, more than 80 percent of primary voters said they would be satisfied with McCain as their nominee - but less than 30 percent would be "very satisfied." The findings suggest a far lower level of enthusiasm than exists among Democratic primary voters, roughly four in 10 of whom would be very satisfied with Clinton or Obama as their nominee.
A majority of Republican primary voters said McCain generally has the right positions on the issues, though self-described conservatives were less enthusiastic: 52 percent said the Arizona senator is not conservative enough.
Almost three-quarters of Republican primary voters - including 60 percent of conservatives - want a candidate who would compromise with Democrats in order to get things done. Only 14 percent said they want a Republican president who will stick to Republican positions even if it means getting less accomplished. A majority said they believe McCain would compromise the right amount as president.