Only 41 percent of Americans said Romney understands their needs and problems, compared to 54 percent who feel Mr. Obama understands their needs and problems.
Romney will have an opportunity to reach out to voters on Thursday when he accepts the Republican nomination for president. In an interview this week, Romney suggested he recognizes this empathy gap and isn't necessarily looking to fix the issue.
"I know there are some people who do a very good job acting and pretend they're something they're not," Romney said. "You get what you see. I am who I am."
In that interview, he also said, "I don't think everybody likes me."
According to the CBS News poll, Romney has a 31 percent favorable and 36 percent unfavorable rating, with 32 percent saying they're undecided or don't know.
Forty-one percent have a positive opinion of Mr. Obama, while 44 percent view him negatively.
Heading into the political conventions, the president and his GOP rival are in a tight race among registered voters who lean towards a candidate. Mr. Obama has just a one-point lead, 46 percent to 45 percent (within the poll's margin of error), with 6 percent undecided.
The president continues to lead among women -- by 10 points in this poll -- while Romney has a nine-point lead among men. In 2008, Mr. Obama won women voters by 13 points (56 percent to John McCain's 43 percent), but the race was much narrower among men. Mr. Obama edged out McCain among men by just one point, according to CBS News Exit Polls.
For the full poll results, see next page.
This poll was conducted by telephone from August 22-26, 2012 among 1,218 adults nationwide, including 1,051 registered voters. Phone numbers were dialed from samples of both standard land-line and cell phones. The error due to sampling for results based on the entire sample and the sample of registered voters could be plus or minus three percentage points. The error for subgroups may be higher. Percentages may not add to 100% due to rounding. This poll release conforms to the Standards of Disclosure of the National Council on Public Polls.