Most of the bombs the Weathermen were blamed for had been placed to do only property damage, a fact Mr. Ayers emphasizes in his memoir. But a 1970 pipe bomb in San Francisco attributed to the group killed one police officer and severely hurt another. An accidental 1970 explosion in a Greenwich Village town house basement killed three radicals; survivors later said they had been making nail bombs to detonate at a military dance at Fort Dix in New Jersey. And in 1981, in an armed robbery of a Brinks armored truck in Nanuet, N.Y., that involved Weather Underground members including Kathy Boudin and David Gilbert, two police officers and a Brinks guard were killed.

In his memoir, Mr. Ayers was evasive as to which bombings he had a hand in, writing that “some details cannot be told.” By the time of the Brinks robbery, he and Ms. Dohrn had emerged from underground to raise their two children, then Chesa Boudin, whose parents were imprisoned for their role in the heist.

Little Influence Seen

Mr. Obama’s friends said that history was utterly irrelevant to judging the candidate, because Mr. Ayers was never a significant influence on him. Even some conservatives who know Mr. Obama said that if he was drawn to Ayers-style radicalism, he hid it well.

“I saw no evidence of a radical streak, either overt or covert, when we were together at Harvard Law School,” said Bradford A. Berenson, who worked on the Harvard Law Review with Mr. Obama and who served as associate White House counsel under President Bush. Mr. Berenson, who is backing Mr. McCain, described his fellow student as “a pragmatic liberal” whose moderation frustrated others at the law review whose views were much farther to the left.

Some 15 years later, left-leaning backers of Mr. Obama have the same complaint. “We’re fully for Obama, but we disagree with some of his stands,” said Tom Hayden, the 1960s activist and former California legislator, who helped organize Progressives for Obama. His group opposes the candidate’s call for sending more troops to Afghanistan, for instance, “because we think it’s a quagmire just like Iraq,” he said. “A lot of our work is trying to win over progressives who think Obama is too conservative.”

Mr. Hayden, 68, said he has known Mr. Ayers for 45 years and was on the other side of the split in the radical antiwar movement that led Mr. Ayers and others to form the Weathermen. But Mr. Hayden said he saw attempts to link Mr. Obama with bombings and radicalism as “typical campaign shenanigans.”

“If Barack Obama says he’s willing to talk to foreign leaders without preconditions,” Mr. Hayden said, “I can imagine he’d be willing to talk to Bill Ayers about schools. But I think that’s about as far as their relationship goes.”