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But among troops, data show, he’s still struggling to win them over.

A Military Times poll conducted early this year found that 31 percent of subscribers to the publication approved of his job as commander in chief, while 53 percent disapproved. Those findings were similar to Military Times poll taken in December 2008, just before Mr. Obama was inaugurated, and found that 32 percent were “optimistic” about Mr. Obama as their commander in chief, while 30 percent were pessimistic and 35 percent were uncertain.

Given that the military is “a fairly conservative lot,” Mr. Obama inevitably faced an uphill battle in winning over many of the rank and file, Mr. Eaton said.

But the president’s stock has risen with moves such as traveling to Dover Air Force Base to be present for the arrival of bodies of troops killed in combat, visiting Walter Reed Army Medical Center to talk with wounded troops, backing commanders’ requests for more unmanned drones and signing the GI bill last summer.

“There is a shift in mood - it’s not a tectonic plate shift, but it’s a drift - the acknowledgment that this president has been very successful in the counterterrorism war that we are waging in Afghanistan, Pakistan, Yemen and Somalia,” he said. “We’ve got a military that is coming to grips with the fact that they have a competent commander in chief.”

That is a change from May 2009, when the new president did an about-face on the release of photos that allegedly showed U.S. troops abusing prisoners, deciding to block their court-ordered release after commanders on the ground said they would set back the war efforts in Iraq and Afghanistan. In September last year, after Gen. Stanley A. McChrystal’s request for more troops in Afghanistan was leaked to The Washington Post, Mr. Obama took heat for taking several weeks to mull it over, eventually issuing orders for a 30,000-troop surge in early December. Mr. Obama fired Gen. McChrystal in June after he and members of his staff spoke indiscreetly in a Rolling Stone magazine article.

Though veterans organizations give Mr. Obama high marks on the policies that matter most to them, they bristled at an early proposal within the administration to require veterans who were wounded in combat to bill their third-party insurers. But Peter Gaytan, executive director of the American Legion, said the episode is an example of the White House’s willingness to listen to and work with veterans groups, who talked officials out of the idea.

“His ability to listen to us, to sit down and talk … shows us that he is willing to do what’s right,” Mr. Gaytan said.

The American Legion has praised Mr. Obama for following through on his promise to boost VA funding. Even amid competing priorities and a deepening recession last year, he secured the biggest budget increase in 30 years. This year, despite proposing a freeze on other domestic spending, he asked for 10 percent more.