President's Reagan's proposed cuts in Social Security and other basic programs for the poor and unemployed won easy approval yesterday in preliminary votes by the Senate Finance Committee and House social security subcommittee.

In a report to the Senate Budget Committee setting forth its intentions for this year, the Finance Committee went unanimously on record in favor of spending cuts of $9.3 billion in programs within its jurisdiction and a tax cut of no more than $51.4 billion for fiscal 1982. Both figures match the president's requests. There was no specific commitment, however, to a three-year tax cut as proposed by the administration.

The votes were the first major tests of resistance to Reagan's proposals to cut back social programs, and they showed the Reagan recommendations have powerful momentum on Capital Hill. Yesterday's votes were not final; they are merely estimates by the panels of the extent to which they will eventually report out legislation cutting outlays. But the pattern was unmistakable.

With Republicans voting as a bloc, the Finance Committee crushed a series of Democratic efforts to moderate Reagan's proposed cuts. Then it unanimously approved Reagan's request that Social Security, unemployment insurance, welfare, social services, Medicare and Medicaid be slashed $9.3 billion in fiscal 1982.

The House social security subcommittee acted without even any Democratic gestures at derailing the budget express. It voted unanimously and by voice vote to recommend that outlays for the one program under its jurisdiction, Social Security, be cut $2.445 billion in fiscal 1982.

The figure is $2 million more than Reagan requested, an addition proposed by Rep. Andrew Jacobs (D-Ind.) as a symbol that while the cut will be as large as Reagan wants, the subcommittee retains the right under budget procedures to make the cut in places that it will designate later in the session, not necessarily in exactly the same parts of the program that Reagan has proposed. The Senate Finance Committee said the same.

After the House subcommittee vote Rep. Willis D. Gradison Jr. (R-Ohio) said he believe the House public assistance subcommittee will also approve cuts in social programs.

Asked why Democrats in the House appeared to be going along with Reagan on cuts in social programs they themselves created and fostered, Gradison laughed: "I think there are two camps. One says let's go along with the president because if we do, he'll be thrown out. The other says if we don't, we'll be thrown out."

In the Finance Committee, the Democrats did put up some resistance but were snowed under by Republican votes, with Chairman Bob Dole (R-Kan.), just back from kidney-stone surgery, orchestrating the action.

Sen. Russell B. Long (D-La.) offered a motion to cut the $122-a-month Social Security minimum benefit only $100 million instead of $1 billion in fiscal 1982, by wiping out the minimum guarantee only for those coming on the rolls in the future, instead of for those already there.

Long, who at times acted as if still chairman of the committee, warned that present recipients of the minimum Social Security payment believe "God meant them to have that money." But his motion lost, 12 to 6, with 11 Republicans and Harry F. Byrd Jr. (Ind.-Va.) voting against, and six Democrats for. A series of amendments to reduce proposed cuts in the low-income energy program and the trade adjustment assistance program were beaten by even larger margins.

Finance Committee members agreed that if Congress does not approve all the spending cuts Reagan has asked for, they may cut taxes by less than the $51.4 billion.