President Reagan hurled another budget thunderbolt at House Democrats yesterday in the form of a proposal for nearly $20 billion more in spending cuts over the next three years, all aimed at achieving more of his economic program than House committees were willing to grant.

Democrats responded with a tentative strategy under which the House would vote on Reagan's plan, but in piecemeal fashion so that members would have to vote separately on each category of cuts, thereby stripping them of the protective cover of Reagan's overall economic program.

The GOP plan, developed jointly by House Republicans and Budget Director David A. Stockman, was shaved back to what its sponsors called "bare essentials' in hopes of overcoming apparently strong loyalty from within both parties to the House committee structure; the Republican plan would in some cases alter drastically the way the established committees cut programs to meet Reagan's budget targets.

The proposed changes cut a broad swath across the budget, mostly in open-ended benefit or entitlement programs. There would be less of a pay increase for federal workers, less of a cost-of-living increase for government retirees, fewer college loans, fewer people on the food stamp rolls, less subsidized housing and fewer school districts sharing in the impact aid bounty, among other things.

For a few favored programs, however, including the Clinch River breeder reactor and the Export-Import Bank, some funds would be restored.

The GOP plan also includes a modified version of Reagan's proposal for consolidating nearly 100 separate federal programs into no-strings block grants to the state, which were largely rejected by House committees and accepted in only watered-down form by Senate committees.

In throwing his weight behind the plan and saying he would apply "gentle persuasion and reason" to get it passed, Reagan said there were "serious shortcomings" in the $37.8 billion package of spending cuts that House committees approved this month in an attempt to meet his slashed-back budget goals.

"Let there be no doubt: we can and we will put a stop to the fiscal joyride in Washington," Reagan said before taking a helicopter ride for the weekend to Camp David.

Specifically, he criticized the omission of block grants, and charged that the committees achieved only one-third of the savings from reining in the big entitlement programs that were contemplated in the budget targets that Congress adopted in response to administration pressure.

Moreover, the Office of Management and Budget charged that "nearly a quarter of the so-called savings have been achieved through accounting gimmicks, inclusion of items that do not belong in a reconciliation bill, unrealistic proposals and wishful thinking."

Denying the charges, House Budget Committee Chairman James R. Jones (D-Okla.) said the Democrats may reverse course and allow a vote on the Reagan alternative on the House floor. But he said the Democrats are leaning toward to a plan to submit each category of cuts to a separate vote, which is what they have been aiming for all along. They think it will be harder for members to vote for cuts one by one than to cast one vote for economy in government generally.

In explaining the plan, House Minority Leader Robert H. Michel (R-Ill.) said it will boost the committees' "real" savings by $5.2 billion in 1982, $7.2 billion in 1983 and $7.3 billion in 1984 -- for a three-year total of $19.7 billion. But even it falls short of meeting the targeted cuts in entitlement programs by about $3 billion.,

Moreover, Stockman told reporters later that it still leaves the administration $4 billion to $5 billion short of cuts necessary to put the government on the road to a balanced budget by 1984, as Reagan has promised.

The administration proposal is aimed only at the Democratic-controlled House because the White House has no apparent quarrel with the Republican Senate's handiwork. It would change the work of seven House committees, leaving the other eight committees' plans untouched.

A more sweeping substitute was under study earlier, before it became apparent that it would have serious trouble, despite Reagan's stunning victory on the budget targets last month.

"Our amendments represent compromise and conciliation but not capitulation," said Michel, acknowledging that even the pared-down proposal would have difficulty in light of historical congressional reluctance to would have difficulty in light of historical congressional reluctance to tamper with the established system. "We're not asking for the whole pie. We are not retiring what the committees have done. We are seeking to improve upon what they have done."

In its "package of amendments," which was pointedly not called a substitute, the Republicans proposed:

Reinforcing a proposed "cap" on food stamp money by tightening eligibility rules, including imposing an income limit of 130 percent of the government-establishd poverty level for families to qualify for stamps. The House Agriculture Committee had imposed the cap in the reconciliation legislation but proposed the eligibility changes separately, which meant the savings were in doubt, according to the Republicans.

Cutting back the subsidized housing program even further than the Banking Committee did, including reducing the number of new units next year from 176,000 to 162,500 and increasing costs to tenants from 25 percent of income to 30 percent of income over the next five years (estimated at $5 per month next year).

Restricting the guaranteed student loan program by requiring that income be taken into account in determining how much money will be loaned for a college education, thereby curtailing aid to middle-income students. The Education and Labor Committee dropped its earlier idea of limiting loans to students from families earning $25,000 or less a year but imposed a 4 percent origination fee for loans.

Allowing cost-of-living increases for civil service and military retirees only once a year, instead of twice a year, as currently provided. The Post Office and Civil Service Committee refused to make this change for civilian workers, and Armed Services approved it for the military only if it was also approved for civilians.

Giving federal workers a pay increase next year of 4.8 percent, rather than the 5.4 percent recommended by Post Office and Civil Service. The reduced level would be in line with the Senate's proposal.

Restricting impact aid for school districts to cover only children of families who live and work on federal installations, at 90 percent of the current entitlement, meaning the Washington area would lose most of its impact aid money. The Education and Labor Committee proposed a formula that would continue money flowing at reduced rates into all districts with government workers.

Continuing "double-dipping" by dropping a committee proposal to deny pensions to military retirees who get civilian government jobs -- a proposal that the Republicans say would save little if anything because the retirees would take jobs elsewhere. A similar provision to eliminate pay for military reserve duty to civilian government employes would also be dropped.

Dropping savings claimed by the Banking Committee for reducing Export-Import Bank loans to U.S. exporters on the theory that the action was "so extreme that that Congress would have to overturn it later."

Restoring funds for the Clinch River breeder reactor, which the House Science Committee had cut out. More government funding would also be included for the Strategic Petroleum Reserve, but this only means that less of the nearly $4 billion for oil stockpiling will be put "off-budget" on the somewhat shaky premise that a way will be found to fund the program from private funds.

Capping Medicaid payments to the states and giving states flexibility to cut their programs to live within the new limits, as the administration wanted. The cap would be indexed to account for inflation. The funding increase for next year would be 6 percent rather than 5 percent, as Reagan proposed.

Increasing savings from phase-out of student benefits under Social Security and eliminating the minimum Social Security benefit, while deleting a committee-approved delay of three months in the cost-of-living adjustment for Social Security recipients.

Tightening methods for computing welfare payments under the Aid to Families of Dependent CHILDREN (AFDC) program.

Targeting school lunch subsidies more toward lower-income children, meaning an overall reduction in lunch subsidies.

Meanwhile, in the less contentious Senate budget arena, Budget Comittee Chairman Pete V. Domenici (R-N.M.) said Republicans and Democrats were making progress in n negotiating their way out of a fight over Democratic demands that "extraneous" legislation be stripped out of the Senate's reconciliation package. Domenici said they were "fairly close" to agreement on proposals from three committees and "still negotiating" about proposals from two others. At stake are such issues as radio-television deregulation and housing aid to cities like Washington and New York that practice rent control.