When President Reagan began slicing into the federal budget, he coined a term to allay fears that the cuts would come at the expense of the elderly, unemployed and poor.

These "truly needy," Reagan assured the nation in his Feb. 18 economic message on "America's new beginning," would be protected by a "social safety net."

This week, Reagan decided to make the holes in that net a little wider.

Though the president said in February that the preservation of the safety net programs, most of which date back to Franklin D. Roosevelt's New Deal, was a high priority transcending ideology, partisanship or fiscal needs, Reagan ran out of places to cut federal spending and came down this month to a simple choice: he could shred the safety net or he could cut back defense spending.

As recently as Tuesday, Reagan promised during a White House reception that "the budget will not be balanced at the expense of those dependent on Social Security."

Yet Reagan and his advisers have now decided on a postponement of cost-of-living increases in Social Security and in at least three other safety net programs--for veterans, retired railroad workers and the needy elderly, aged and blind--as well as food stamps and some other programs, to cut costs in the fiscal year beginning Oct. 1.

At the Reagan White House, there always has been a distinction between "the truly needy" and others. The implication is that a large group of not truly needy people have been living off the federal government and that these freeloaders are the only ones who will suffer in days of lessened federal spending.

The president cited his experience with welfare while he was governor of California. Using figures that are disputed by some of his California critics, Reagan often tells audiences that when he tightened up California welfare programs thousands of people simply disappeared from the rolls.

The implication is that they survived quite well without welfare, that they were welfare cheats, untruly needy.

In all, the Reagan administration says it will save $5 billion in 1982 by a one-time postponement of cost-of-living increases in inflation-indexed programs.

White House communications director David Gergen told reporters during Reagan's trip here to dedicate the Gerald R. Ford presidential museum that Reagan's commitment to protect the truly needy is unchanged.

In a briefing during which Gergen was careful not to call the pension reductions "cuts," Gergen quoted Office of Management and Budget Director David A. Stockman as saying that the average loss per person for Social Security recipients will be less than $100.

Last winter, when Reagan began to cut into federal spending, there was large popular support for his effort. Reagan was particularly pleased by responses such as a letter from an unemployed Illinois man who wrote that he was happy to give up his unemployment compensation as part of the president's effort to restore the economy.

This winter, Reagan's economic program will be working, and it remains to be seen how many of those who lose federal benefits will share that attitude.

This month has brought the beginning of a change of perception. In the beginning, cutting the budget was a numbers exercise. The president told the nation it was an essential task, and most Americans, in the spirit in which they make New Year's resolutions or start on diets, agreed.

Now, the numbers are being translated into details which are sometimes mean. For example, there will be fewer ounces of milk and meat for children in school lunches. Ketchup will be called a vegetable. Welfare recipients will be audited to make sure they don't have assets worth over $1,000. And now pensioners, who in states like Florida, Arizona and California voted for Reagan last November, may also pay a price.

Reagan knows as well as any politician the perils of attacking Social Security. During last year's campaign, former president Carter again and again brought up Reagan's statements from the 1960s indicating that he then favored a voluntary Social Security system.

Reagan had been hurt by such charges in earlier campaigns, but he successfully rebutted them last year, pledging himself to preserve Social Security.

Reagan and his advisers also are well aware how politically explosive their effort to hold down retirement benefits can be. After the Cabinet meeting at which Reagan made his decision known, Gergen told reporters dryly: "It was agreed by all concerned that this was going to be a difficult undertaking."

At the same time, Reagan's spokesmen are no longer so comfortable speaking of their "social safety net." The term has fallen into disuse.

Is the net intact? Gergen was asked.

"I think it's only fair that the president...have an opportunity to discuss and address that kind of issue once you see the program as laid out," he replied. "There's no question that the emphasis is to maintain vital services," he added.

The safety net initially was a symbol, and the symbol has changed now that the seven programs--Social Security retirement benefits, Medicare, railroad retirement, basic unemployment compensation, welfare, veterans' benefits and supplemental security income for the elderly, blind and disabled--have lost their immunity. The change puts Reagan in a different position.

The net, of course, protected Reagan as well as the needy. It helped deflect criticism.

Rents in the net open a new political season for the president.