President Reagan tries harder than most politicians to keep his promises, but he has broken his share in the past and will find it necessary to do so again.

After the performances of Reagan and his predecessor, President Jimmy Carter, it may be a long time before any presidential candidate promises to balance the federal budget. Both Reagan and Carter promised this in their first presidential campaigns, and neither came close to doing it. Not only that, Reagan presides over the largest peacetime deficit in U.S. history.

He has followed the trail blazed by his first political role model, Franklin D. Roosevelt, who ignored some of his more realistic advisers and promised in a 1932 campaign speech in Pittsburgh to balance the budget, if elected.

Instead, Roosevelt did what was wise and necessary; he offered deficit-financed plans that began the long path of recovery from the Depression. When the question arose as to how FDR should reconcile what he was doing with his Pittsburgh pledge to balance the budget, a speech writer gave advice that became famous: "Deny you were ever in Pittsburgh."

Reagan made a triad of important and contradictory promises in his 1980 campaign. He pledged to "restore the nation's defenses," to cut income taxes across the board and to balance the budget. He kept the first two promises, thus increasing his problem in keeping the third.

In this year's campaign, Reagan promised even more. He pledged not to raise taxes and to push for tax simplification that would produce no additional revenues. He promised to seek more domestic spending cuts. He promised that there would be no cuts in Social Security or in the defense budget.

The defense-spending promise is a trap door through which many billions of dollars in spending reductions could fall. Real growth in defense spending averaged 9 percent annually during Reagan's first term. Secretary of Defense Caspar W. Weinberger is proposing a 14 percent increase in the coming fiscal year.

The question in 1985, as it was in 1981, will be which promise should be set aside in order to save the others. The obvious answer to many of Reagan's fellow Republicans is that he should treat defense spending the way he does domestic spending and propose cuts in both to dent the deficit.

The case for cutting defense is being made most eloquently by Republicans who have been staunch supporters of the president and of military spending. The new Republican Senate leadership, more mindful than Reagan of the realities of the deficit, favors a slowdown in military spending. This mood is even more prevalent among the restless Republican minority in the House.

"If Ronald Reagan is ever going to deliver on his promise to reduce the size and scope of government, this is his last shot," said Rep. Dick Cheney (Wyo.), a member of the House Republican leadership. "I don't think he can do it unless he will take a whack at defense. If he is willing to give up on defense, he can be very tough on vetoes."

Rank-and-file Republicans are similarly inclined. Rep. Connie Mack 3d (R-Fla.), a second-term member, says he would have difficulty asking his south Florida constituents to make sacrifices unless the Pentagon is willing to do likewise.

Cheney argues that taking a whisk broom to domestic spending and a feather duster to defense gives Republicans no leverage on domestic spending and leaves them open to the charge that they are kinder to bombers than to babies. And it is tactically unproductive because the administration usually winds up making compromises that rescue the defense budget at the cost of keeping domestic programs the Democrats want to protect.

Weinberger, skilled in the ways of Washington negotiation, has always asked for more than he expects to get. But this tactic may have outlived its usefulness, if the House reaction is any gauge.

House Republican Whip Trent Lott (Miss.), an outspoken hawk, put it bluntly last week in response to a question about Weinberger's proposal. "They've got to come in at a more likely level, no more than 7 or 8 percent," he said. "At 12, 13, 14 percent, everybody knows it's a high bid, and it just won't work."

Reaganism of the Week: Posing with the next Senate majority leader, Sen. Robert J. Dole (R-Kan.), at the White House last week, Reagan said, "I'm not going to take any questions. I'm just looking pretty for the cameras."