The normally sympathetic Senate Armed Services Committee began public hearings on President Reagan's proposed $258 billion defense budget yesterday with members plainly looking for quick cuts, and just as plainly having trouble finding them.

Republicans Gordon J. Humphrey of New Hampshire and Dan Quayle of Indiana and Democrat J. James Exon of Nebraska all cautioned Deputy Defense Secretary Frank C. Carlucci that cuts would be coming and essentially asked him where he thought they should be made.

Carlucci, who has just spent several months working on the budget, would not help. He rejected the idea that there is any padding in the defense spending plan, saying it is an "honest" budget which is especially large in part because the Pentagon is trying to be "up front" about the real costs of weapons and inflation.

While searching for soft spots, moreover, these senators wanted assurances from Carlucci that the $70 billion requested for operations and maintenance of the military next year--money to train troops and keep equipment combat-ready--would be stoutly defended by the Pentagon. In the past this has often been the first category to be cut.

This reflects one of the big dilemmas faced by lawmakers who believe the defense budget is too large. Operations and maintenance are tempting targets to cut because cuts there show up immediately and help reduce the deficit. Cuts in more visible individual weapons, on the other hand, yield much smaller immediate savings because spending for those projects is spread over many years.

But cutting back on readiness is precisely what Congress does not want to do, so Carlucci quickly agreed that such reductions, even though appealing for budgetary reasons, would be "unconscionable." And to buttress his case that cutting the big weapons projects also doesn't help much, Carlucci said that cutting all $19 billion in spending authority this year for the MX missile, B1 bomber, Trident submarines, two new aircraft carriers and cruise missiles would save only about $5 billion in actual spending or outlays.

Quayle and Exon persisted, however, warning Carlucci that cuts would come-- probably "substantial" ones, Exon said--because there is much less support outside the normally friendly Armed Services Committee than there is inside it.

Sen. Carl Levin (D-Mich.) leveled the strongest blast at the Pentagon, describing the record budget as "a declaration of economic war on America" that would ultimately undermine security because it would overrun the economic foundation that security is built on. Levin charged that the huge new military budget and lopsided administration priorities will "give defense a bad name and will end up eroding public support" for defense.

He characterized as "hollow" Carlucci's claims that Pentagon management initiatives would save $50 billion that might have otherwise been spent on defense in the next five years. Levin said some $24 billion of that is due to a government-wide civilian pay cap that has nothing to do with any Defense Department initiative.

The Reagan-run Pentagon also came in for sharp criticism yesterday from a group of former Pentagon officials of the Carter administration who call themselves "Democrats for Defense." Here, too, however, the concern is that Congress not succumb to simple across-the-board cuts that would affect readiness. Rather the group mentioned as worthy of congressional scrutiny the B1 bomber, the two new nuclear-powered aircraft carriers, what was called an overemphasis on shipbuilding, and the Reagan plan to reverse the decision of four previous administrations by again building up defenses against bomber attacks in the missile age.

The group, which includes former deputy secretary of defense Robert W. Komer and two other assistant secretaries of defense, said the plan to increase defense spending has merit but is inconsistent with the huge deficit and revenue cuts and is thus apt to lead to a vain and unwise congressional round of cuts.