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“I am extraordinarily grateful that he has agreed to serve in this new capacity,” said Mr. Obama, adding he was doing so “at great personal sacrifice to himself and to his family,” and was “setting an extraordinary example of service and patriotism by assuming this difficult post.”

Senate hearings have been scheduled for next Tuesday.

The Petraeus nomination was “a politically very savvy move,” Mr. Finel said, because “it should neutralize any criticism from the right. He is the master of counterinsurgency.”

Nonetheless, while personally praising Gen. Petraeus, some Republicans voiced their anxiety about the task he was taking on, given the escalating violence in Afghanistan and what some regard as an arbitrary and dangerous deadline set by the president to begin withdrawing U.S. troops next summer.

“General Petraeus is an outstanding military leader,” said Sen. Christopher S. Bond, Missouri Republican and the ranking member of the Senate Select Committee on Intelligence, “but even he can’t win in Afghanistan if the president continues to insist on an arbitrary withdrawal date — a fact our enemies are counting on and our allies fear.”

Mr. Finel said the timeline the president demanded would be “easy to fudge.”

“You send one brigade home, but you extend a couple of others and before you know it, you have as many troops there as ever,” he said.

He added that, having been asked by the president to take what is in many ways a step down, Gen. Petraeus would have “tremendous leverage.”

“It will be very, very hard to refuse him anything he asks,” Mr. Finel said, adding that he expected a “shake up of senior people in Kabul, with a number of people who were close to McChrystal [leaving.]”

Though his words were far more politic than Gen. McChrystal’s, Gen. Petraeus told Congress at a hearing last week that Mr. Obama’s July 2011 target date to start pulling U.S. forces from Afghanistan should be put off until the security situation in Afghanistan was ready to handle such a pullout.