Barack Obama's campaign fired back Sunday against John McCain's ad accusing him of snubbing Hillary Clinton for his running mate slot, calling the attack "demonstrably false."

The ad, released at 3 a.m. Sunday, suggested that Obama did not choose his former rival because she pointed out his character flaws during the Democratic primaries.

"She won millions of votes. But isn't on his ticket. Why? For speaking the truth," the narrator in the ad says. "The truth hurt. And Obama's didn't like it."

The ad sought to exploit tension between Obama and Clinton's supporters -- tension that continued to simmer after officials confirmed that Clinton was not even vetted for the vice presidential slot. Obama gave that job to Delaware Sen. Joe Biden Saturday. 

Clinton released a statement Sunday saying her support of Obama is "clear" and that it's "interesting" McCain chose not to include in his ad her remarks praising their shared commitment to getting troops out of Iraq and providing access to health care.

Obama spokesman Robert Gibbs, speaking with "FOX News Sunday," also disputed reports of lingering divisions in the party, claiming the Democratic National Convention -- which begins Monday in Denver -- will show a united front.

"Senator Obama had a great conversation with Senator Clinton this week as well as former president Bill Clinton. Everybody's on board," he said. "And it's going to drive the media crazy when we come out of this convention united. ... Hillary Clinton, Joe Biden, everybody that ran for this office is going to be united."

Gibbs and Obama strategist David Axelrod slammed McCain's camp for the new ad.

"They know that that ad is demonstrably false," Gibbs said. "They know that Hillary Clinton is supporting Barack Obama."

Axelrod told ABC News' "This Week" that McCain only opens himself up to even harsher attacks with his ad, since McCain is reportedly strongly considering former rival Mitt Romney for his running mate. Romney and McCain engaged in a fierce battle in the closing weeks of the Republican primary.

"You could fill your whole show with the nasty things ... that John McCain and Mitt Romney said about each other just a few months ago," Axelrod said.

He disputed reports that Obama left Clinton out of the loop on his running-mate decision, saying "the first person that he sat down and talked to at all about this vice presidential issue was Senator Clinton alone."

Axelrod also described Biden, who's been in the Senate for more than three decades, as a Washington outsider at heart.

"He's never lived a day in Washington, D.C.," he said.

Virginia Gov. Tim Kaine, who was considered as a finalist to be Obama's running mate, described Biden as a blue-collar champion.

"They can run any attack ad they want but here's the issue: Americans want a change in the direction of this nation," he told "FOX News Sunday." "Joe's a guy who grew up in a working-class household ... They both understand the experience that Americans are going through now."