The change, approved on Tuesday by the Senate as part of its annual defense policy bill, would apply across government and affect thousands of veterans and their close relatives, who also are able to jump the line over non-veterans.

It was high-level Pentagon officials who pressed Sen. John McCain (R-Ariz.), chairman of the Senate Armed Services Committee, for a change to the veterans hiring system. These officials have expressed concern to McCain and other lawmakers that too many qualified non-veterans are getting shut out of federal jobs in deference to those who served but may not be qualified for some positions, according to Senate staff.

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The veterans language has flown under the radar in a bill with thousands of provisions. But it’s now fiercely opposed by leading service organizations, which had no idea until the legislation was on the floor that the Senate was moving to chip away at the government’s most visible effort to reward military service since the draft ended in the 1970s.

“Is Congress now starting to dial back the goodwill the country’s shown toward veterans’ employment?” asked Lauren Augustine, senior legislative associate for Iraq and Afghanistan Veterans of America, an advocacy group. “Are we now going to set a bad example to the private sector by limiting veterans preference in government?”

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But McCain and other committee members are acknowledging privately that it is time for the well-intentioned policy to be tweaked, committee aids say. Preference for veterans has caused resentment and confusion among veterans and non-veterans over whether the leg up is applied fairly and whether it is bringing the best people into government.

McCain, who spent five and a half years in a North Vietnamese prison cell during the Vietnam War, said in a brief hallway interview in the Capitol that he did not know about the policy change in the bill. But, aware of the sensitivity around hiring veterans, he said, “I’m sure we would never” erode preference policies.

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McCain later clarified his position and reiterated his belief that the change would not undermine veterans’ preference.

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“We must balance the goals of rewarding those who are eligible for a federal hiring advantage with the needs of the federal government and notably the Department of Defense to attract and hire the best talent for a variety of important national security jobs,” the senator said in a statement.

The defense bill “achieves this balance by ensuring veterans still have the ability to get a foot in the door for federal civilian employment, after which they stand on merit,” McCain said.

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Almost 1 in 2 people hired to permanent federal jobs are veterans, with former service members making up 47.4 percent of new hires to full-time positions in fiscal 2014, the last year for which the government is provided data. Starting in 2009, Obama boosted the extra credit veterans get to give them a greater edge in getting federal jobs, setting hiring goals for veterans at each agency and directing managers to be graded on how many former service members they bring on board.

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But Defense Department officials have told senators that pressure to hire veterans is forcing them to fill some jobs in procurement, acquisitions, science and technical offices with former service members when a non-veteran may be a better fit, Senate aides said.

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“This was considered the best way to capture the intent to tweak the policy without causing emotional alarm, a step to get the conversation going,” said a Senate aide involved in negotiations over the change who was not authorized to speak publicly.

Defense Department officials declined to comment on the proposed change because the legislation is pending.

Veterans service groups said they oppose efforts to erode a benefit designed to help former service members who lost valuable time developing their civilian careers while they served their country.

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“While you’re serving, you have a different breadth of experience,” said Ian de Planque, legislative director for the American Legion.

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“Veterans preference is working,” he said. “It’s not been something we’ve ever heard of as being problematic.”

The American Federal of Government Employees, the largest federal employee union, also said it opposes the change.

Hiring experts said the real problem is not with veterans themselves but with how the preference law is applied. Job candidates are separated into lists based on their qualifications, which are reflected by a score out of 100 points. Experience, veteran status and scores on the candidates’ multiple-choice self-assessment of their skills determine the scores. In each category (most qualified, well-qualified, qualified), veterans go to the top of the list.

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But the top category that hiring managers draw from is often too broad,experts say, and can include candidates who are significantly less qualified than others. “Only the crème de la crème should be on that list,” said Jeffrey Neal, former human capital chief at the Department of Homeland Security and now a senior vice president for ICF International, “whether they are veterans or not.”

The measure will go to a conference committee between the Senate and House, whose version of the defense bill does not include the changes to veterans preference.

A spokesman for the House Armed Services Committee said lawmakers have not yet taken a position on the hiring language. But the chairman of the House Committee on Veterans’ Affairs was skeptical that preference for veterans is leading to unqualified hires.

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“The way veterans preference works is that when a hiring decision comes down to two equally qualified candidates and one is a veteran, the veteran gets hiring preference,” Rep. Jeff Miller (R-Fla.) said in a statement. “Anyone who believes otherwise is misinterpreting the law.”

Karoun Demirjian contributed to this story