House GOP leaders announced yesterday they plan to propose a Republican alternative to the pending Democratic budget resolution, calling for a $20 billion tax cut beginning in 1980 and $21 billion in spending cutbacks.

Minority leader John J. Rhodes (R-Ariz.) said the proposal -- which is decidedly less restrictive than some GOP members have sought -- was designed to attract support from moderate and conservative Democrats.

Earlier GOP efforts to challenge the Democrats' budget proposals have failed in part because they were too conservative for the majority of the House.

Rhodes said the new GOP alternative would seek a spending level of $528 billion, compared to $549 billion in the House Budget Committee's recommendation, with a deficit of $20 billion -- $9.2 billion below the Democrats' plan.

However, Rhodes and other GOP leaders who discussed the package yesterday refused to disclose details of which programs would be cut under the proposal for $21 billion worth of spending holddowns.

The GOP leaders also declined to provide any breakdown of the $20 billion tax cut package, except to predict that about $5 billion of that total would be used to allow business faster depreciation writeoffs.

Rhodes said the details would be unveiled after the proposal is formally approved Tuesday by the House Republican Policy Committee. The budget resolution is scheduled to come to the floor later next week.

The concerted effort by the Republicans represents a new twist in GOP budget strategy in the House. Traditionally, Republicans have been too splintered among a spate of budget cutting proposals to muster a firm majority.

GOP leaders also are counting on widespread dissatisfaction among House members at the Budget Committee's recommended $29 billion deficit, which is $6 billion above the red-ink figure that Congress approved last spring.

Budget Committee leaders say the increase is primarily caused by higher inflation and unemployment costs. However, critics say even the $29 billion figure is artifically low, pared from $34 billion by some last-minute maneuvering.

The developments came as, separately, Senate Democratic leaders failed for the second day in a row to reach an agreement on how to end an impasse over that chamber's budget resolution, clouding prospects for passage of the measure.

The tentative budget targets that Congress set last spring included assumptions for $5.6 billion in "cost saving" measures, but so far the lawmakers have enacted only a few of these.

Now they are faced with the choice of cutting back appropriations bills they already have passed or accepting a higher deficit than the $28 billion the Senate Budget Committee recommended. The move has touched off a major fight.

The Republicans' proposal for a tax cut in the House was designed to steal the thunder from the Democrats, who so far have been siding with President Carter in contending that no tax cut is needed and it would only fuel inflation.

Rep. Barber B. Conable (R-N.Y.), ranking Republican on the House Ways and Means Committee, asserted yesterday that any tax cut "ought to be timed to have the maximum impact when it can do the most good for the economy."