OXFORD, Mississippi (CNN) -- A national poll of people who watched the first presidential debate suggests that Barack Obama came out on top, but there was overwhelming agreement that both Obama and John McCain would be able to handle the job of president if elected.

The CNN/Opinion Research Corp. survey is not a measurement of the views of all Americans, since only people who watched the debate were questioned and the audience included more Democrats than Republicans.

Fifty-one percent of those polled thought Obama did the better job in Friday night's debate, while 38 percent said John McCain did better.

Men were nearly evenly split between the two candidates, with 46 percent giving the win to McCain and 43 percent to Obama. But women voters tended to give Obama higher marks, with 59 percent calling him the night's winner, while just 31 percent said McCain won.

"It can be reasonably concluded, especially after accounting for the slight Democratic bias in the survey, that we witnessed a tie in Mississippi tonight," CNN Senior Political Researcher Alan Silverleib said. "But given the direction of the campaign over the last couple of weeks, a tie translates to a win for Obama." Watch entire debate: Part 1 » | Part 2 » | Part 3 »

McCain apparently failed to get the "game changer" he needed to reverse his deficit in the polls, Silverleib said. Grade the candidates' performances in the debate

Both candidates appeared to exceed expectations. McCain did better than expected in the minds of 60 percent, while 57 percent said Obama did a better job in the debate than they expected. Twenty percent said both candidates did worse than expected. iReport.com: Who do you think won the debate?

More than two-thirds of debate watchers agreed that both McCain and Obama would be able to handle the job of president if elected.

National security has been an issue where McCain has held an advantage, but his edge over Obama -- 49 percent to 45 percent -- on the question of which candidate would best handle terrorism is within the poll's 4.5 percent margin of error. Watch candidates discuss likelihood of another 9/11 »

The economy, which has been Obama's terrain this cycle, dominated the first half of the debate. Debate watchers gave him a 21 percentage point edge -- 58 to 37 percent -- on the question of which candidate would do a better job handling the economy.

By a similar margin, those polled said Obama would be better able to deal with the current financial crisis facing the nation. Watch McCain, Obama discuss the economy »

The real impact of the debate may not be apparent right away.

"The real test will come in a few days when we see whether support for Obama or McCain changes in polls involving all voters, not just debate watchers," said CNN Polling Director Keating Holland.

"In post-debate polls after the first faceoff in 2004, John Kerry got virtually the same numbers as Obama did tonight. Polls released a few days later showed Kerry gaining five points in the horse race."

Good post-debate poll numbers don't always spell success in the horse race, he said.

"Kerry also won the third debate in 2004 with the same numbers that Obama got in tonight's poll, but his support dropped five points after that event," Holland said.

Poll interviews were conducted with 524 adult Americans who watched the debate and were conducted by telephone on September 26. All interviews were done after the end of the debate. The margin of error for the survey is plus or minus 4.5 percentage points.

The results may be favoring Obama simply because more Democrats than Republicans tuned in to the debate. Of the debate-watchers questioned in this poll, 41 percent of the respondents identified themselves as Democrats, 27 percent as Republicans and 30 percent as independents.

The best estimate of the number of Democrats in the voting age population as a whole indicates that the sample is roughly 5 to 7 percentage points more Democratic than the population as a whole.

CNN's Rebecca Sinderbrand contributed to this story.

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