Congress, unwilling to be seen as inflicting any kind of pain on the military or veterans, rejected the increases. Mr. Gates said he got the message  “The proposals routinely die an ignominious death on Capitol Hill,” he said in May  and he did not try again in 2010. But in shaping that budget proposal, Obama administration officials also told the Pentagon not to raise it, lest it distract from Mr. Obama’s overhaul of the nation’s health care system earlier this year.

Some Pentagon officials and military advocacy groups have suggested alternatives to raising fees that could cut costs. One idea is to renegotiate the lucrative Tricare packages with the insurance companies, hospitals and drug companies that actually operate the programs. Another is to promote a cost-saving mail-order pharmacy.

Defense officials say that Mr. Gates has to make up his mind about any health care fee increases in the next weeks, in time for the Pentagon to submit its 2012 spending plans to the White House budget director in December. Defense analysts who spoke to Mr. Gates over the summer said he told them that he did not know if it was realistic to try to increase military health care costs while troops were at war.

But Defense Department officials have since said they see a window of opportunity in the growing alarm over the federal debt, the focus of two bipartisan panels that are proposing deep cuts in government spending.

Mr. Gates met in recent weeks with the leaders of one of the panels, former Senator Alan K. Simpson, a Republican, and Erskine B. Bowles, a Democrat and the former chief of staff to President Bill Clinton. They are the co-chairmen of Mr. Obama’s fiscal commission, which has proposed raising Tricare fees. The panel is trying to deliver a final report to the White House on Wednesday, if the members can reach a consensus that fast.

The panel is considering proposals to increase fees for military retirees working for civilian companies, but it would also require employers to reimburse the government for a share of the health insurance costs of those on their payroll who opt for Tricare. That measure alone, described as an effort to make civilian employers pay “a normal business expense,” could recoup $3 billion annually for the Pentagon.

In the meantime, Colonel Brady, 51, said he did not want to be overly dramatic about what was at stake. Although he spent 22 years in the Marines, six of them deployed, including to the 1991 Persian Gulf war, he said he could not buy the argument about a broken promise.