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Senators are pushing to reinstate tuition assistance for members of the U.S. military, decrying a move by the administration to suspend the program citing the sequester.

"The president wants Americans to feel the pain of the arbitrary across-the-board budget cuts from sequestration, but to cut off promised education assistance for our service members when there are other lower priority spending programs to draw from is an injustice," Sen. Jim Inhofe, R-Okla., top Republican on the Senate Armed Services Committee, said in a statement.

He and Democratic Sen. Kay Hagan of North Carolina introduced an amendment Wednesday to a stopgap budget bill that would restore the program. Inhofe told Fox News he has additional Democratic support lined up, and warned that dropping the program not only hurts service members -- it could hurt the military as a whole.

"It would hurt retention and our ability to enlist these people," he said.

Inhofe said the tuition assistance, at least in the Army, is a major motivation for people to enlist.

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"They can work a little bit harder and be able to get a college degree, and for them to pull that out from under them ...." Inhofe said.

He acknowledged the administration needs to make cuts to comply with the sequester -- the across-the-board cuts that took effect March 1 -- but suggested the Defense Department shave back its "green agenda" to find the money.

Hagan, in a statement, also said she understands the Pentagon has some "tough budget decisions" to make, but called the decision to suspend tuition assistance "shortsighted."

So far, the Army, Marines and Air Force have pulled back on the program for this fiscal year.

The Marine Corps said in a statement that it is trying to preserve "essential programs" and that leadership "remains committed to providing opportunities to Marines as they pursue their educational goals."

"Education counselors are available to assist Marines with their education choices including providing information about other education programs," the statement said, noting there are "other education funding options such as the GI Bills, grants, scholarships and loans that can support a broader continuum of learning and educational goals."

The Army program gives soldiers as much as $4,500 annually to take courses, at accredited schools, toward high school and college diplomas. Army officials could not give a specific amount on how much the cuts would save, but said 201,000 soldiers used the program in fiscal 2012 at the cost of $373 million.

Administration officials have been challenged on a host of sequester-related cuts, from a decision to release low-priority illegal immigrants from southwest jails to a decision to suspend White House tours.

President Obama indicated Wednesday that he was reconsidering the tour decision, and trying to find a way to let in student groups. Generally, administration officials maintain they're doing the best they can in trying circumstances, noting that even though the cuts amount to roughly 2 percent of the federal budget, they're applying to only a portion of that budget -- and must be squeezed into the remaining seven months of the fiscal year, making the impact more pronounced.

Meanwhile, a petition on the White House website to reinstate military tuition assistance has recently surpassed 100,000 signatures, which typically triggers an official response from the White House.

"Access to Higher Education is important to Service Members as it allows for career and professional advancement," the petition says.