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Rep. Howard P. “Buck” McKeon, California Republican, told Adm. Mullen at a Feb. 3 hearing, “This position in support of repeal comes before your service chiefs have had the opportunity to conduct an in-depth review of the impact a repeal would have on military readiness. It seems that your path places the cart before the horse.”

Pressed later at the House Armed Services Committee hearing on the chiefs’ positions, Adm. Mullen said, “I don’t speak for the chiefs in that regard. They will have an opportunity to do that. I have discussed this with them at considerable length. I would sum up their view to say that they need to understand that impact as well should this policy change.”

Mr. Gates has acknowledged that the chiefs have worries about open gays in the ranks. That is one reason he ordered the study to see what impact the significant social change would have on readiness and unit cohesion — the bonding of war fighters.

The study, he said, “is precisely so we can understand not just the views and concerns of the chiefs, but of our military people and their families. And the impact on unit cohesion, on morale, on retention, so we understand what these things are so we get some facts into this debate. Or at least some data that we think is reliable and objective.”

Last week, Mr. Gates defended the need to study the issue first. He also said he wants to avoid putting more stress on an already stretched force.

“I think this has to be done very carefully and very deliberately,” Mr. Gates told Fox News Channel’s “On the Record.”

“The military culture is a very strong one,” he said. “It’s a very different culture than a civilian culture. These people do not have choices about who they associate with. They can’t just up and walk off the job if they don’t like somebody that they’re working with. And so we have to take all that into account, it seems to me. And I know people say I’m just delaying or whatever, but I think this is a big change for the military, and it has to be done in a careful way. We have a force that’s been under stress for eight years, been at war for eight years. And I don’t want to do anything that makes the situation more difficult for those men and women in the fight.”

Robert Maginnis, a retired Army officer and conservative commentator who worked on the homosexuality issue while at the Pentagon in 1993, said Adm. Mullen jumped the gun.

“It’s critical the chiefs remain objective about the homosexual issue,” he said. “Unfortunately, Adm. Mullen abandoned his objectivity when he gave his personal opinion before launching the task force to examine the issue. The chiefs must understand many, if not most, service members are skeptical about [President] Obama’s promise to repeal the law. They understand he owes the gay lobby a debt and the military is expected to pay the price.”

But a new poll shows that opposition is waning. The Military Times newspapers reported that a survey shows opposition to open gays in the ranks dropped from 65 percent in 2004 to 51 percent today. The Times surveyed readers via e-mails and questionnaire inserts.

A CBS/New York Times poll this month found that 44 percent of Americans say homosexuals should be allowed to serve openly. They may now serve as long as they keep their sexuality private. However, a poll press release said support dropped compared with a year ago, when 67 percent voiced approval.

When the word “homosexual” is replaced with “gay men and lesbians” in the new poll, the percentage rises to 58 percent who approve.