President Reagan's new proposal to cut Social Security benefits ran into a Democratic firestorm yesterday, with House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) branding them "despicable" and vowing to "fight them all the way."

Meanwhile, it was learned that Budget Director David A. Stockman, seeking still more cuts, is considering proposing to the president that this year's 11.2 percent cost-of-living increase in Social Security benefits be postponed from July to Oct. 1.

The three-month deferral would push about $4 billion in spending from fiscal 1981 into fiscal 1982 and thereby lower the 1981 deficit, which Stockman is anxious to cut. The president Tuesday proposed deferring cost-of-living increases starting next year, but made no mention of this year's.

O'Neill, one of many angry Democrats to denounce the president's proposals yesterday, called them a "breach of faith" in light of earlier Reagan promises to keep hands off the old-age program. "I'm talking about the decency of it," he said. "It's a rotten thing to do."

Asked if the president's proposals would win approval, O'Neill said acidly that he doubted that any members of Congress would be "stone-hearted enough" to vote for them. His stance was in marked contrast to his position on the president's general budget cuts last week. O'Neill had virtually accepted those as inevitable.

The churning on Social Security came as the Senate Agriculture Committee, in a victory for Reagan, backed off its budget-busting votes of last weeks ago and approved a new farm bill much closer to the president's proposals.

In another victory for the president, the House last night approved, 329 to 70, and sent to the Senate legislation rescinding $12.7 billion of past appropriations for this fiscal year.

And in still another development, the administration's tax-cut proposals met resistance in the Senate Finance Committee, where members indicated at a hearing that they intended to cut back the president's proposal and substitute some alternatives of their own.

Sen. Russell B. Long (D-La.), ranking Democrat on the panel, bluntly warned Treasury Secretary Donald T. Regan that the administration would have to give Democrats a hand in shaping the tax bill if he wanted their support. But Reagan continued to side-step on the question of compromise.

Meanwhile, Democrats on the House Ways and Means Committee, in a separate caucus, agreed broadly not to support Reagan's plan for a three-year, 30 percent across-the-board cut in income tax rates, but remained undecided on what kind of alternative to back instead.

The House Democrats' anger over the Social Security cuts was vented repeatedly in floor speeches. Rep. James M. Shannon (D-Mass.), typical of many, recalled that the president had promised to leave Social Security alone as part of a "safety net" for the needy, and shouted: "He has gone too far. It's time we stood up."

At the White House, acting press secretary Larry Speakes insisted that Reagan didn't want to propose Social Security cuts, but was "faced with a stark reality: either do something or the system will go under. I think we have done the best we can," he said.

A Ways and Means Social Security subcommittee did approve $2.6 billion in smaller benefit cuts yesterday, mostly proposed by Reagan earlier. But these affect relatively minor aspects of the program, such as student benefits, and subcommittee members cautioned their action did not mean they would approve the much larger 10 percent cut in Social Security costs that Reagan proposed this week.

Rep. Richard A. Gephardt (D-Mo.) complained it would be "bordering on the unethical" to cut pensions for those about to retire, one of the main new Reagan proposals.

In the Finance Committee hearings on the tax bill, Chairman Bob Dole (R-Kan.) reiterated his earlier warning that the president did not have enough support among members for his full proposal, but administration officials refused to give in.

Regan, insisted that "the president sees no need to change his program," appealed to committee conservatives to postpone their tax proposals until the administration puts together a second tax bill, to be submitted before Congress' August recess.

Only two panel members -- Sen. William V. Roth (R-Del.), one of the original architects of the president's tax-cut plan, and Sen. Steven D. Symms (R-Idaho) -- formally endorsed Reagan's three-year tax-cut plan at yesterday's hearing.

Regan also had to fend off fears by panel Democrats that the president's tax-cut plan would fuel the budget deficit and inflation -- a charge that forced him into the unlikely position of being a republican defending red-ink budgets.

"There is no evidence per se that deficits cause inflation," the treasury secretary said in response to a charge by Sen. Daniel P. Moynihan (D-N.Y.). Regan also dismissed concerns over Wall Street's sour reaction to the program, saying "the bond markets have been in disarray for months."