His Republican rival, John McCain, interviewed on Wednesday for CNN's Larry King Live programme, said he believed any issues of race in America would be eclipsed by the economic problems facing the country.
Most Americans would "vote on who they want to lead the country", he said.
Economic crisis 'temporary'
Earlier, surrounded by a dozen former military officers and national security advisers at a rally in Tampa, Florida, McCain told crowds: "The question is whether this [Obama] is a man who has what it takes to protect America from Osama bin Laden, al-Qaeda and the other great threats in the world.
"He has given no reason to answer in the affirmative."
McCain said the campaign's focus has understandably been shifted from national security to economics, but warned that did not mean dangers from abroad have passed.
He argued that the economic meltdown, while serious, was temporary.
Both US presidential candidates had taken their election battle to the crucial state of Florida on Wednesday.
New polls have indicated Obama maintains a strong lead over his Republican rival in four previously Republican states and is tied in two others ahead of the vote on November 4.
Obama, who also holds a strong lead in several national polls, began the day in Raleigh, North Carolina, before he headed to Florida to appear alongside Bill Clinton, the former US president.
"The presidential campaign is the greatest job interview in the world. And on Tuesday, you get to make the hire," Clinton said as he introduced Obama at their first ever joint event.
Obama, who praised the former president as a "political genius", said it was time to replicate the successes of his presidency.
"It's time for the kind of peace and prosperity that we saw in the 1990s," Obama added. "We've dug a deep hole, and George Bush wants to turn the shovel over to John McCain."
McCain renewed his attacks on Obama's financial plans, saying they would hurt small business, and calling his Democratic rival the "redistributor-in-chief".
"Senator Obama is running to spread the wealth. I'm running to create more wealth," McCain told supporters in Miami.
"Senator Obama is running to punish the successful. I'm running to make everyone successful."
In North Carolina, Obama retaliated, saying McCain's economic proposals would be bad for America's middle class and would continue the Republican policies of George Bush, the US president.
"He's spending these last few days calling me every name in the book. I'm sorry to see my opponent sink so low," Obama said before heading to Florida for his own campaign events.
"By the end of the week, he'll be accusing me of being a secret communist because I shared my toys in kindergarten."
Florida, which has 27 electoral college votes, voted Republican for the past two elections but recent polls indicate that Obama is tied with McCain.
The candidates need to capture 270 college votes out of 538 in order to win the US election, as the national popular vote does not determine the winner.
Al Jazeera's Rosiland Jordan, reporting from Miami, says Florida is a "must-win" state for McCain, with 10 per cent of the votes needed to win the election, and his camp has been telling supporters not to trust the polls as they claim they can pull off a surprise win in the state on November 4.
The AP-GFK poll, released on Wednesday, has Obama leading in the state of Ohio by seven percentage points, in Nevada by 12 points, Colorado by nine points and Virginia by seven points.
All were previously Republican states won by George Bush, the current US president, in 2004's election.
In addition, the poll shows Obama is tied with McCain in North Carolina and in Florida, two states also carried by Bush in 2004.
Nationally, a poll by the Pew Research Centre a day earlier gave Obama a 16-point
lead among registered voters, with 52 per cent compared to McCain's 36 per cent.
Other nationwide polls have shown Obama holding a lead in single digits.