Biden made the remarks Thursday in response to a question from a woman who attended his forum on national security and veterans issues in military-heavy Virginia Beach. The questioner said she realized it's tricky for a male candidate to debate a woman but implored Biden to "please promise me you'll go after her the same way...."
The rest of the question was drowned out by applause and cheers.
"The way I was raised is: I never, ever, ever attack the other person," Biden said, adding that probably was not what many of his fellow Democrats want to hear. "I will take issue with her as strongly as I can."
Biden said that has been his approach through 13 presidential debates.
"I'm not good at the one-line zingers. That's not my deal," Biden said.
Palin's speech accepting the vice presidential nomination at the Republican National Convention was packed with zingers, and Biden said he was impressed with the way she delivered it.
"I think she's going to be an incredibly competent debater," he said.
In an appearance on "The Early Show", Biden told co-anchor Maggie Rodriguez, "I was impressed. I think it was a skillfully delivered political speech with confidence and directness and so I think she did what she was supposed to do.
"…I was also impressed by what I didn't hear in the speech. I didn't hear the word-the phrase-"middle class" mentioned. I didn't hear about health care. I didn't hear a single word about what we're going to do about the housing crisis-college education-all the things that the middle class is being burdened with right now."
He said in response to another question in Virginia Beach that the middle class would be better off economically under Democrat than Republican .
"Ninety-five percent of American households' taxes will go down," he said. "If you're making $250,000 a year - and I hope you are - we don't have a tax cut for you."
Economic issues were on the agenda for a forum later in the day in Manassas, Va. The morning event was dominated by veterans and military matters. Those are big issues in the region, which is home to several military installations, including the world's largest Navy base.
The military presence would seem to benefit McCain, a former Navy aviator who spent more than five years as a prisoner of war in Vietnam. McCain refused offers of early release and returned home on crutches and unable to lift his arms.
Biden said he's never known anyone more courageous than McCain, his longtime Senate colleague, but he said Obama already has demonstrated better judgment on military and foreign policy matters. It's a claim Biden has been making to counter Republican criticism about Obama's lack of experience.
"Experience only matters if you couple it with judgment," Biden said.
Brigadier Gen. David McGinnis, chief of staff of the National Guard Association and one of six participants in the forum, said he believes Obama is well qualified to be commander in chief because he has a strong grasp of strategy.
"He has a demeanor that is unbelievably cool," McGinnis said.
Biden also said the nation's leaders have a "sacred obligation" to care for the soldiers they deploy and the ones who come home - an obligation he said the Bush administration has not met.
Earlier on Thursday, Obama's top strategist dismissed Palin's prime-time convention address as dishonest about Obama's record and suggested that McCain's running mate was only parroting what she'd been told.
David Axelrod told reporters aboard Obama's campaign plane that the Republican National Convention speakers on Wednesday had distorted the Democratic candidate's record and ignored his resume. He also signaled that the Democrats would not hesitate to take on McCain's running mate.
"There wasn't one thing that she said about Obama or what he's proposing that is true," Axelrod said. "She tried to attack Senator Obama by saying he had no significant legislative achievements. Maybe that's what she was told."
On Wednesday, Republicans as untested and inexperienced, making light of his past work as a community organizer in Chicago.
"For everyday people, ... that seems like real work," said Axelrod.
Ultimately, Axelrod said, the Republicans squandered an opportunity to promote their candidate. He also questioned the emphasis on McCain's years as a prisoner of war, saying the Arizona senator's history already was well known.
"They're shedding an awfully lot of heat but no light," he said. "It almost defies the laws of physics."
As for Palin's claim to be an outsider, Axelrod said that given her pointed criticism of Obama, "for someone who makes the point that she's not from Washington, she looked very much like she would fit in very well there."