The agency's push toward streamlined applications appears to be having an impact. The VA is receiving about 700 fully developed claims a day, representing roughly 10 percent of all claims, according to agency data. That's up from about 3 percent of all claims filed in January.

Shinseki, who was wounded in Vietnam, has vowed to eliminate the claims backlog by 2015.

To accomplish that goal, the agency has focused mainly on replacing its paper claims with an electronic system. During their meeting on Capitol Hill last week, Shinseki, Hagel and Acting Social Security Administration Commissioner Carolyn W. Colvin also vowed that their agencies would work more closely together on the issue.

The American Legion, headquartered in Indianapolis, was created in 1919 to help veterans returning from World War I. Its nationwide membership has declined in recent decades as many other groups have been created, but it nevertheless retains 2.4 million members.

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"They earn benefits," Hagel said. "They deserve, at the end of that career, those benefits.

"You take care of your people. It's that simple."

VA's claims backlog

A look at the percentage of VA claims pending for more than 125 days.

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Jan., 2012: 79.2 percent // 65.5 percent

Dec., 2012: 83.3 percent // 67.6 percent

May, 2013: 81.5 percent // 66.9 percent

Source: U.S. Veterans Administration