"If the needs of the families can be met, and the privacy concerns can be addressed, the more honor we can accord these fallen heroes, the better," said Gates at a news conference at the Pentagon last week. "I'm ... pretty open to, to whatever the results of this review may be."
Just Friday, Pentagon spokesman Geoff Morrell said Obama might hear back from Gates in "a matter of days, rather than weeks."
Military families say that if the ban is lifted, they hope that individual wishes are respected and the issue does not get further politicized.
"Our stand is always on the side of the families," said Joe Davis, a spokesman for Veterans of Foreign Wars of the U.S. "How they choose to honor the service and sacrifice of their loved one is a family decision, one in which outsiders with different agendas should have no influence."
Military Families United, which represents about 60,000 such families, has asked the Obama administration to consult their group before shaping public policy. So far, they have had no response.
"If there needs to be a change, it should be up to family members to decide," said President John Ellsworth. "Those who are affected should make that call."
"Some want to show honor and want to be able to share their hero with America," he told ABCNews.com. "Others would rather hold it a little closer."
Ellsworth, 45, knows the pain firsthand -- his 20-year-old son, Justin, was killed in an explosion in 2004 in Iraq and he was awarded numerous medals for saving 11 others in the blast.
Lance Corporal Justin Ellsworth joined the Marines in 2003, inducted just hours before the March invasion of Iraq.
"We were visiting Washington, D.C., in August 2001, and two weeks later the Pentagon steps were in smoldering ruins," said he father. "It really affected him."
"If it's not me, Dad, who is it going to be?" asked Justin. When Marines arrived at Ellsworth's door at 10:15 on Saturday night, he knew it was "bad."
"It absolutely changed my world," he said. "I was a small-town cop in the middle of Michigan and had no idea how government worked. But dealing with this, I felt a need to help military families."
But Ellsworth refused to say that Bush "wanted to hide" the war deaths. "We don't want it to become political on either side," he said.
Sondra Millman-Cosimano of Riviera Beach, Fla., is worried the effort will be hijacked by anti-war groups. She lost her granddaughter, Airman First Class Elizabeth Jacobson, in an explosion. The 21-year-old was the first female security officer to die in Iraq.
"It's wrong to exploit it," she told ABCNews.com. "We need to honor what they gave for their country. It's a touchy thing. And the media can only take a picture and then everyone else puts their spin on it.
"It seems to be the people who have the most to say are not the ones who have lost a loved one," according to Cosimano, 68, a former police dispatcher.
"War is not a good thing but it's part of life," she said. "I believe in law, honor, honesty and country."
She does agree that "when you see a bunch of coffins coming back, you get a different image of what it's about," she said.
But New Mexico insurance saleswoman Hope Veverka, 49, said President Bush "should not have kept those moments secret," referring to the ban on photos of returning caskets.