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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.
President Obama and Mitt Romney are effectively tied in the race for the presidency, according to a new CBS News/New York Times survey.
Forty-seven percent of registered voters nationwide who lean towards a candidate back Romney, while 46 percent support the president. Four percent are undecided. The 1 percentage point difference is within the survey's three-point margin of error.
Romney leads by eight points among men; the president leads by five points among women.
The president's supporters are more likely to strongly back their candidate. Fifty-two percent strongly favor Mr. Obama, while just 29 percent of Romney voters strongly back the presumptive Republican nominee.
More than one in three Romney voters say they are supporting Romney primarily because they dislike Mr. Obama. Only eight percent of Obama supporters say their support for the president is tied to their dislike of Romney.
Republicans are more enthusiastic than Democrats when it comes to voting in this election, though just one in three registered voters overall are more enthusiastic than they were in the past. Roughly half of Republicans say they are more enthusiastic compared to past elections - up from 36 percent in March - while just 27 percent of Democrats say they same.
One in five registered voters with a candidate choice said they still might change their mind. The percentage of those willing to switch was essentially the same for both candidates.
Forty-five percent of registered voters say they are paying close attention to the campaign, and another 38 percent say they are paying some attention. Seventeen percent say they are paying little or no attention.
Fifty-four percent of registered voters cite the economy and jobs as "extremely" important in their presidential vote, more than any other issue. Here Romney has the edge: 49 percent of registered voters say he would do a better job handling the economy and jobs, while 41 percent cite Mr. Obama.
Romney is also seen as better on the federal budget deficit (50 percent to 36 percent), taxes (47 percent to 42 percent) and illegal immigration (46 percent to 38 percent). Mr. Obama as seen as better on foreign policy (47 percent to 40 percent) and social issues (48 percent to 37 percent). Views of the candidates on health care and terrorism were split.
Thirty-eight percent of registered voters say Mr. Obama cares a lot about their needs and problems, compared to 25 percent who say the same of Romney. Registered voters were slightly more likely to say that Mr. Obama says what he believes (45 percent) than to say that Romney says what he believes (37 percent).
Only 28 percent believe Mr. Obama has fulfilled his promise to deliver positive change for the country. Fifty-eight percent say he has not delivered change, while 7 percent say he has delivered change that has been bad for the country.
Mr. Obama's overall approval rating stands at 44 percent, with 46 percent disapproving. His approval rating on the economy is just 39 percent - 55 percent disapprove - and his approval rating on foreign policy is 41 percent. His approval rating on the economy has dropped five points since April.
Both candidates have net unfavorable ratings. Forty-eight percent of registered voters view the president unfavorably, while 36 percent view him favorably. Romney is viewed unfavorably by 36 percent and favorably by 32 percent. Nearly one in three say they do not yet have an opinion about the presumptive Republican nominee.
Seven in 10 Americans say the economy is in bad shape. While 24 percent say it is getting better - down from 33 percent in April - 30 percent say it is getting worse. That marks the highest percentage who say the economy is getting worse since December.
Two in five Americans say they are very concerned someone in their household will lose their job.
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.