The spat over Google Voice, along with other confrontations, sharpened one of Google’s worst fears: that a rival could keep millions of people from accessing its services. A Google executive vowed to bring Google Voice to the iPhone “one way or the other,” and the company quickly developed a workaround to circumvent the Apple block.

If anyone could negotiate a ceasefire, it would be Bill Campbell, a well-regarded Silicon Valley business counselor known simply as Coach.

Mr. Campbell, a former college football coach and the former chief executive of Intuit, has played pivotal roles at Google. He sat in on high-level management meetings, counseled Mr. Schmidt individually in private sessions every other week, helped to establish the company’s management structure, and had a hand in smoothing over the initially turbulent relationship between Mr. Schmidt and Google’s founders.

Mr. Campbell also looms large at Apple, where he is co-chairman of the board, and was one of the few people in whom Mr. Jobs confided during his health crisis.

While Mr. Campbell has tried to be a diplomat and smooth over the problems between Mr. Jobs and Mr. Schmidt, the task hasn’t been easy. Mr. Campbell declined to comment for this article, but people briefed on the matter say that throughout last fall, Mr. Jobs and Mr. Schmidt each lobbied Mr. Campbell to sever his connection with the other’s company, at times even giving him ultimatums to do so.

Finally, Mr. Campbell was forced to choose, and according to a person with knowledge of the situation, he dropped his formal responsibilities at Google, although he is still informally mentoring executives there.

Mitch Kapor, the founder of Lotus Development and now a tech investor, describes such infighting as “old wine in a new bottle,” and reminiscent of many past corporate battles in Silicon Valley. He sees the old dynamics between Apple and Microsoft being recycled, with Apple still trying to control every aspect of the user experience, and Google, like Microsoft before it, working with multiple partners to flood the market with a large number of devices.