Forty-nine percent of likely voters said they would pick Obama if the election were held now and 47 percent said they would vote for Romney, results of the poll released Monday indicated.
Obama leads Romney by 5 percentage points, 49 percent to 44 percent, among registered voters.
Results indicate Obama has a 52 percent-to-41 percent advantage over Romney among likely voters in swing states, mirroring Obama's edge in recent Post polls in Florida, Ohio and Virginia.
Results indicate a majority of voters view Romney's wealth as a positive, while fewer said they are focusing on economic inequality and the gap between rich and poor, the Post said. Results also indicate a large number of voters say they think Romney has paid his fair share in taxes.
More than seven in 10 voters said they are dissatisfied or angry with the way the federal government is working, results showed.
Obama maintained double-digit leads on questions of who's more friendly and likable, and is seen as more trusted on social issues, women's issues and terrorism.
The president also leads when it comes to empathy with people experiencing economic problems and is seen as the one who could better handle "an unexpected major crisis."
He and Romney were viewed evenly on the deficit, healthcare and Medicare, results indicated.
On the economy the two tied at 47 percent.
Results are based on a nationwide telephone survey of 1,101 adults conducted Wednesday through Saturday. The results have a margin of error of 3.5 percentage points for the sample of 929 registered voters and 4 percentage points for sample of 813 likely voters.
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