Biden added that he has met with a "really apologetic" McChrystal.
"I was the guy who, in fact, was their problem, they thought," Biden said. "I'm not their problem. I agree with the policy the president put in place."
Biden said McChrystal's team thought he was the enemy because he had laid out a plan for U.S. involvement in Afghanistan "that was different in degree."
At a future date, Biden promised, his plan would be released and all would become clear.
"Someday, I'll be able to lay out exactly what the plan I offered was," Biden said. "It would be inappropriate to do that because it was so close to what, in fact, the plan ended up being that there was virtually no difference. But I got characterized because I was really very challenging to some of the assertions made."
The vice president recounted a recent side conversation he had with Petraeus during a meeting in the White House Situation Room after Petraeus agreed to become the new commander in Afghanistan.
"I pulled him aside and I said, 'David, there is no daylight between your position and mine.' And he said, 'I know that. Will you tell people that?' And I said, absolutely I'd tell people that," Biden said. "So there's ... a split that has been advertised that far exceeds anything that occurred from the beginning of this reconsideration."
Biden also revealed that after the Rolling Stone article was released, he consulted a number of top generals and they were unanimous: McChrystal had to go.
"It was clear: I was asked to and I did on my own survey, I think, six four star generals, including present and former," Biden said. "Every single one said he had to go.
"So ... the president made the right decision," Biden said. "He changed the personalities, but not the policy. He put the strongest guy in the U.S. military and a counter-insurgency policy in place. It was the absolutely necessary thing to do."
To many Democrats, their prospects this November are looking rather bleak. Respected congressional prognosticator Charlie Cook says that Democrats will lose 30 to 40 seats in the House and five to seven in the Senate. A recent ABC News poll put Americans' confidence in congressional Democrats to make the right decisions for the country at 32 percent.
But to Biden, things are looking up.
"I don't think the [Democratic] losses are going to be bad at all," Biden said. "I think we're going to shock the heck out of everybody.
"I am absolutely confident [that] when people take a look at the what has happened since we've taken office in November and comparing it to the alternative, we're going ... to be in great shape," he said.
"What I believe, what the president believes [is that] we're going to win the House and we're going to win the Senate. We're not going to lose either one of those bodies," Biden said.
Asked if he thinks elements of the Tea Party are racist, Biden seemed to equivocate at first, but then settled on a firm no.
"Well, the truth is that at least elements that were involved in some of the Tea Party folks expressed racist views," he said.
"I wouldn't characterize the Tea Party as racist," he added. "There are individuals who are either members of or on the periphery of some of their things -- their protests -- that have expressed really unfortunate comments.