The change has fueled speculation in Washington about whether General Petraeus might seek the presidency in 2012. His advisers say that it is absurd — but in immediate policy terms, it means there is one less visible advocate for the military in the administration’s debate over whether to send up to 40,000 additional troops to Afghanistan.

General Petraeus’s aides now privately call him “Dave the Dull,” and say he has largely muzzled himself from the fierce public debate about the war to avoid antagonizing the White House, which does not want pressure from military superstars and is wary of the general’s ambitions in particular…

How much General Petraeus’s muted voice will affect Mr. Obama’s decision on the war is unclear, but people close to him say that stifling himself in public could give him greater credibility to influence the debate from within. Others say that his biggest influence may simply be as part of a team of military advisers, including General McChrystal and Adm. Mike Mullen, the chairman of the Joint Chiefs of Staff.