The narrow gap represents a sharp difference to a similar Pew poll conducted two weeks ago, before the first presidential debate. At the time, 51% expected Obama to fare better, while 29% said Romney would walk away as the night's winner.
Obama's debate performance at the University of Denver was widely panned compared to that of Romney, who gained a modest bounce after the match-up. The two candidates face off for the second time Tuesday at Hofstra University in Hempstead, New York. CNN Chief Political Correspondent Candy Crowley will moderate the debate.
The Pew poll also found that independent voters have stronger expectations for Romney than they did two weeks ago. Forty-two percent of independents say Romney will win, while 31% think the president will fare better. Before the first debate, Obama was expected to win among the voting bloc, by a 44% to 28% margin.
Some of the president's campaign advisers on Sunday predicted a stronger, more assertive performance by Obama for this week's debate.
"He knew when he walked off that stage, and he also knew as he watched the tape of that debate, that he has to be more energetic," adviser Robert Gibbs said on CNN's "State of the Union."
David Axelrod, another Obama campaign adviser and former White House official, said on "Fox News Sunday" that Obama would be "aggressive in making the case for his view of where we should go as a country."
Some, however, acknowledged that the upcoming debate's town hall format may prove difficult for the two candidates to enter attack mode.
"It requires very good interaction with those people and the ability to be able to connect. You have to be able to come across as very likable in a town hall," Republican strategist and CNN contributor Ana Navarro said, adding that one of Obama's strengths is his ability to communicate with average people.
For the survey, Pew interviewed 1,006 adults, including 857 registered voters, between October 12 and October 14. The poll has a sampling error of plus or minus four percentage points.