NASHVILLE, Tennessee (CNN) -- Just hours before the start of the second presidential debate, a new national survey suggests that Sen. Barack Obama is making gains among Americans as a compassionate candidate.

A new poll out Tuesday shows Sen. Barack Obama as a more compassionate politician.

That could be important in the debate in Nashville, which is a town hall-style meeting with the candidates fielding questions from undecided voters in the audience.

In a new CNN/Opinion Research Corporation poll out Tuesday afternoon, 55 percent of registered voters questioned say that Obama "cares more about people like you" than Sen. John McCain, with 35 percent saying McCain cares more than Obama. That 20-point margin for Obama is up from a 9-point advantage a month ago.

"The all-time champion of town-hall debates was Bill Clinton because he was able to connect with the audience members so well," said CNN polling director Keating Holland. "Voters nationwide seem to feel some connection with Obama. The question is whether he'll connect with the people at the debate tonight. John McCain has a pretty good track record at town halls, and it's possible that he will be the one who looks more compassionate."

Obama also appears to be building a lead as the candidate with the clearer plan to solve the country's problems.

He has a 15-point lead over McCain on that question in the poll, 48 percent to 33 percent. Last month, McCain had a 2-point advantage over Obama on the topic of having a clearer plan.

"Debate watchers -- particularly moderates and independents -- tend to look for specifics," Holland said. "Both candidates will probably want to play into that expectation."

Obama's also making gains on being a strong and decisive leader. A 19-point McCain advantage early last month has now shrunk to a 5-point lead. But on the question of who has the better experience to be president, McCain still has a big lead over his rival, 54 percent to 36 percent.

On the issues, voters now think Obama would better handle the war in Iraq than McCain, 51 percent to 46 percent. That's a difference from our last poll.

"Voters agree with McCain that things are going well for the U.S. in Iraq. That's a switch since April, when we last asked that question," Holland said. "But voters also agree with Obama that the war was a bad idea -- and they haven't changed their minds on that in almost four years."

"Iraq may be doing better, but we're not. Guess which matters more to voters," said CNN senior political analyst Bill Schneider.

Among voters, Obama also leads on who would better handle the economy, 57 percent to 37 percent; a financial crisis, 53 percent to 36 percent; and health care, 60 percent to 33 percent. McCain leads on the issue of terrorism, 54 percent to 44 percent. Watch more on the candidates and the economic crisis »

Obama's favorable rating among those questioned in the poll is 62 percent, down one percentage point from three weeks ago. McCain's favorable rating is 54 percent, down three points from three weeks ago.

The CNN/Opinion Research Corporation poll was conducted Friday through Sunday, with 1,006 adult Americans questioned by telephone. The survey's margin of error is plus or minus 3 percentage points for some questions and plus or minus 4.5 percentage points for others.

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