Washington (CNN) -- Sen. John Kyl, one of the members of the special congressional committee set up to create a $1.5 trillion budget-reduction plan, said Thursday those cuts should come out of programs like Medicare and Social Security -- not defense.

The Arizona Republican told a luncheon event by conservative groups the American Enterprise Institute and the Heritage Foundation that the defense budget has been cut enough already, most recently this summer when the debt-reduction deal meant up to $400 billion in defense cuts.

"Defense should not have any additional cuts," said Kyl, who also told the group that he would quit the special committee rather than consider further defense cuts..

"In a $3.5 trillion budget -- two-thirds of which is entitlements -- there is enough slop in the system, that you can find $1.5 trillion in savings without deeply cutting into benefits or totally readjusting how these programs work, although they will require some adjustment," Kyl added.

Sen. Lindsey Graham, R-South Carolina, told the group that the debt-reduction deal -- which created the special committee -- "is a philosophical shift that I'll have no part of."

"What I'm not willing to do as a Ronald Reagan Republican is put on the table cuts in defense that would say to the country and the world at large (that) defense is a secondary concern when it comes to Washington spending. This pisses me off beyond belief," Graham said.

Freshman Rep. Allen West, R-Florida, a retired Army lieutenant colonel who served in Operation Desert Storm as well as in the more recent wars in Iraq and Afghanistan, said he saw first-hand during the budget reductions that followed the fall of the Soviet Union what defense cuts can do to the military.

"When I was a battalion executive officer, we (would) have to start budgeting toilet paper in barracks. We have folks, friends of mine, that were in armored units that could not go out and practice tank tactics. They had to use golf carts to practice tank tactics, because, number one, we couldn't afford the fuel. Number two, we couldn't afford the spare parts," West said.

He said he is worried that the United States isn't paying attention to possible future threats. "Egypt, Syria, Libya are going to cause new security concerns and strategies that the United States of America has to be able to contend with," West added.

But even some of the Republican lawmakers who spoke passionately about protecting the Defense Department from more cuts admitted that there is room for some careful trimming.

"How do we buy weapons? The more it costs, the longer it takes, the more you make, is silly. So we need procurement reform," Graham said. "We've got to look at a retirement system where people live to be 80, you retire at 38, even though you served your country well. I'm willing to do big things."

Sen. Kelly Ayotte, R-New Hampshire, said she agrees that there are ways to trim the Defense Department budget without risking national security. "A third-year law student could negotiate better contracts on behalf of the United States of America than some of the contracts I have seen where we are doing procurement on behalf of our country," she declared.

The urgency of having the special committee find $1.5 trillion in budget cuts is that otherwise the debt deal requires that huge cuts called "sequestration" kick in automatically to programs including defense and Medicare.

But both Graham and Kyl pledged that they would do their best to stop the mandatory across-the-board budget reductions.

"I would do my best to see that it never took effect; in other words, that we would waive it," Kyl said. "This is one where we would have to waive, and so I would do my best to prevent sequestration on defense."

Graham said, "Let everybody pay a little bit if we can't get our act together in Washington, and not take it out of the hide of those doing the most to defend us."