House Democratic leaders yesterday proposed an alternative to President Reagan's economic program that embraces three-fourths of Reagan's proposed spending cuts but keeps at least some money flowing into numerous Democratic-authored social programs that Reagan had marked for extinction.

David A. Stockman, Reagan's budget director, promptly labeled it "unacceptable," and House Republicans, angling for support from Democratic conservatives, prepared to go to the mat for their president.

The Democratic program anticipates less of a tax cut than Reagan wants and, as a result, a smaller deficit than Reagan projects -- holding out the hope of a balanced budget next year, a year before Reagan has said it would be possible under his program.

It proposes to restore more than $7 billion of the money that Reagan would cut next year from social programs, rescuing agencies like the Legal Service Corporation and Economic Development Administration from the bureaucratic graveyard and adding at least a little more money for everything from the arts to veterans' benefits.

Education, nutrition, job training and social services would be among the major gainers. The Democrats also would not "cap" Medicaid for the poor.

Money for social spending would be recouped in part from the huge increase in defense spending that was recommended by Reagan. The Democratic proposal would cut $4.3 billion from military outlays but still leave the Pentagon with a 21 percent increase in spending authority next year. The Democrats also anticipate $4.8 billion in savings from greater governmental efficiency and $2.8 billion less in debt payments because of the smaller deficit.

Using economic and spending assumptions different from those the administration used, the Democrats figure their spending program for fiscal 1982 will cost $4.3 billion less than Reagan's: $713.5 billion rather than $717.8 billion. Reagan had calculated his budget at $695 billion, but the Democrats said this was based on too optimistic a view of the econmy.

Largely because their tax cut would cost $38 billion in contrast to the $54.6 billion price tag they put on Reagan's, the Democrats calculate their deficit at $24.6 billion -- contrasted with $54.6 billion for the Reagan deficit. Reagan calculates his deficit at $45 billion.

The program -- a politically fine-tuned document aimed at attracting conservatives with a slimmed-down deficit while nailing down liberals with more money for social programs -- was announced by House Budget Committee Chairman James R. Jones (D-Okla.) and hailed as a "fairness package" by House Speaker Thomas P. O'Neill Jr. (D-Mass.)

But it drew quick fire from the ranking Republican on the Budget Committee, Rep. Delbert Latta (R-Ohio), a down-the-line supporter of the Reagan program. It is a "high-tax budget," protested Latta, complaining also that it would "dismantle" Reagan's economic program.

Jones' proposal represents the Democrats' best -- and probably only -- shot at modifying Reagan's budget. The Republican-controlled Senate virtually rubber-stamped Reagan's plan last week, brushing aside all Democratic efforts to restore funds that Reagan would cut. While the House is still under Democratic control, it has a bipartisan right-of-center majority, with Democratic conservatives holding the balance of power.

Budget Committee member Leon E. Panetta (D-Calif.) said he expects that all Democrats on the committee with the "possible exception" of conservative Rep. Phil Gramm (D-Tex.) will go along with the Jones alternative, which would ensure its success in the heavily Democratic committee. But Panetta was less sure about the House floor, saying it depended on the degree of active support by Democratic conservatives. And Gramm, a leader among the conservative Democrats, said later he will oppose the Jones alternative unless it is changed.

Bowing to the popularity of Reagan's budget-cutting program in Congress, Jones swallowed many of Reagan's budget cuts whole, ranging from proposed savings of $3.6 billion from ending the large public service jobs program to $50 million in savings from eliminating the Solar Energy and Conservation Bank. The $122-a-month minimum Social Security payment would be ended for all new recipients in 1982 and for everyone in 1983, as would one of two cost-of-living increases received by federal retirees every year in their pensions. The Democrats would reduce water-project funding even more than the administration wants.

But for most programs that Reagan would scrap or slash heavily the Democrats proposed at least at little more money, in some cases just enough to keep the programs alive.

They would save the Legal Services Corporation and the Economic Development Administration but at reduced spending levels. They would reject the cap on Medicaid payments to states, which Reagan proposed in order to save $1 billion.

Among other things, they would add $1.1 billion for child nutrition, $650 million for food stamps, $850 million for low income fuel assistance, $300 million for veterans' health care, $150 million for preventive medical care, $450 million for job training $150 million for trade adjustment assistance, $600 million for social services, $300 million for coal miners' black lung benefits (offset by increased charges for mine operators), $300 million for Conrail, $650 million for educational programs and college loans and $200 million for Amtrak. They would put back 75,000 of the 85,000 units of subsidized housing that Reagan proposed to cut.

For the education, health and social service programs that Reagan would consolidate into block grants, they proposed less of a cutback in spending -- about 10 percent instead of 20 to 25 percent, according to O'Neill.

In some cases, the Democrats proposed more cuts than Reagan did. For instance, they proposed funding the Strategic Petroleum Reserve at a level of $1.5 billion, less than half the $3.9 billion that Reagan proposed. The Senate had cut the reserve's funding by $3 billion. The House Democrats also proposed to cut $1.8 billion by eliminating the July 5.3 percent pay raise for the military. They would cut revenue sharing by $100 million, double Reagan's proposed savings of $100 million from user charges for pleasure boats and plan for $200 million in saving from lower Medicare hospital costs.

The House Budget Committee intends to complete action on the proposal this week, and House floor action is expected late this month. House-Senate differences will be ironed out in conference. Then the two houses will still have to act on scores of bills carrying out the budget.

Stockman, Reagan's budget director, called a news conference late yesterday to challlenge many of Jones' numbers. Stockman called the Jones budget "a very artful package," but concluded that it would be "unacceptable" to the Reagan administration.

Stockman said three aspects of the Jones budget were particularly "objectionable": the cuts it proposes in defense spending, which Stockman said would reduce actual readiness; the delay and dilution Jones implicitly proposed for tax cuts, and "questionable" savings to finance restorations of some social welfare programs.

Stockman said some of the savings Jones proposes to make would never materialize. He also opposed any restoration of the cuts Reagan has proposed in social welfare programs, saying any new savings that are found should be applied to reducing the deficit further.