"We've reached the point here where the message is going to transcend racial divides," Webb told Face The Nation host Bob Schieffer. "There are clear distinctions between Barack and John McCain on issues of intellect, meaning the way you shape the larger issues that are facing the country rather than this tax bill or that tax bill. There are issues in terms of composure and vision.
"I don't see the first African-American candidate; I see someone here who has got the intellect, has got the composure, who can help us bring a formula now together where we can start breaking apart this calcification that has happened [in Washington], where the middle class has been hurt so bad."
Rep. Charles Rangel D-N.Y., also believes that most voters will look beyond Obama's race when deciding whether to support him for the presidency, although he admitted there would be people who may not vote for him because he's an African American. "That's America, and there are people that feel so insecure," he said.
But Rangel also believes that Obama has captured the hearts and the votes of many people who are not African-Americans, which he called "amazing," and who have a purpose larger than prejudices.
"The American people will put race aside and say, 'Let's get out of this problem that Bush has put us in.'"
What November represents, Webb thinks, is a transitional election in which Obama may help forge "a new coalition," including voters who had previously left the Democratic Party, or are disaffected with the Republicans.
"I wouldn't be that worried about the fact that a large percentage of this vote went to Hillary," Webb said. "We need to give Hillary some credit here. You know, she comes from a very strong organization and she has a great record with working people.
"Not only is Barack going to be able to reach out and get a significant percentage of that vote, but he's going to be able to reach back into the Reagan Democrats, of which I was a part, and bring in people who had voted for George W. Bush in the past."
Howard Wolfson, the communications director of Hillary Clinton's campaign, also said Obama's ability to energize voters - and McCain's willingness to repeat Bush administration policies - will bolster the Democrats' chances.
"I think we can't afford a third George Bush term," Wolfson said. "John McCain is running to be the next George Bush. We can't have that in this country. The economy is spiraling into recession; John McCain says more of the same. We've got terrible problems in Iraq; John McCain says more of the same.
"We need a fundamental change, a fundamental break. And I think Barack Obama offers that. And I think the American people are going to respond very affirmatively to that."
Roger Simon, chief political columnist for Politico.com, said McCain has two major challenges: "He has to show first and foremost that he's not going to be George III. But at the same time, he has to build a little enthusiasm.
"The contentious campaign that's been on the Democratic side has energized Democrats. They've registered more people, they brought more people to the polls, they've raised more money. John McCain has to capture some of that spark and enthusiasm on the Republican side. He's got to build some energy. He's got to start doing it now, culminating at the Republican convention at the beginning of September, and then going on to Election Day.
"He's got an unpopular war. He's got a bad economy. But he's also got two selling points: He says he's going to be much more effective in protecting America from terrorism, and he promises lower taxes and says Barack Obama is going to raise taxes."
Read the full "Face the Nation" transcript here.