Budget director David A. Stockman said yesterday that the only alternative to the budget-cutting plan developed by the White House and Senate Republicans is "a whopping big tax increase."

In an apparent attempt to bring wavering Republicans into line in the week before the Senate opens debate on the package, Stockman said Republican candidates would benefit more in the 1986 election from a strong economy than they would be hurt by the anger of constituents who lose Social Security cost-of-living increases, passenger trains and other domestic programs.

Senate debate on the package opens April 22. The Democratic-controlled House, apparently seeking to force the Senate to deal with the painful cuts first, postponed for at least a week budget hearings that had been scheduled this week.

Stockman, appearing on NBC-TV's "Meet the Press," acknowledged that there is powerful opposition to the plan, designed to cut $52 billion from the $200 billion-plus yearly federal deficit. But he said he thinks that senators will see that there is "no other choice."

Both Republicans and Democrats plan amendments to preserve specific programs, particularly the Social Security cost-of-living increase. And House Majority Leader James C. Wright Jr. (D-Tex.) said on CBS-TV's "Face the Nation" that the House will "try to make the sacrifices a little more evenly shared."

But Stockman said that any changes in the plan would cause it to unravel and that "those who would contribute to the unraveling ought to come clean with the American people and tell them what the choice is."

"The alternative is a whopping big tax increase on everybody," Stockman said. "That's something the people don't want and something our economy can't afford. So we either have this big housecleaning, we scale back government to the bare minimum -- the essentials we have to have domestically for our people, internationally for our security -- or we have a whopping big tax increase . . . . "

The White House-Senate GOP package would eliminate the federal subsidy of Amtrak, rural loan programs, the Small Business Administration and Urban Development Action Grants and cut or restrict student loans, Medicare and Medicaid, and operating subsidies for public housing projects. It would allow a 3 percent growth in military spending beyond inflation.

The most controversial proposal, however, would limit the automatic cost-of-living increase for recipients of Social Security and several similar programs. Under the plan, recipients would get an increase for the first 2 percent of inflation, and for any inflation above 4 percent. That would result in a maximum loss, compared to current law, of 2 percentage points if inflation were 4 percent or more.

Stockman argued that "most of the elderly people in this country recognize the day of reckoning has come" and are willing to accept the 2 percent limit for the next three years.

He conceded that the changes in Social Security could be considered "tampering," but he denied that the plan violates President Reagan's campaign promise not to reduce Social Security benefits.

"I don't think it's a broken promise" he said. "The president clearly said that the basic system that protects 35 million elderly in this country would stay intact . . . . But I would point out that the average Social Security recipient or retired couple today is receiving $9,300 a year and even with the restraint we need in order to get this budget under control, they'll have a $560 increase to cover the cost of living over the next three years. So it's not 100 percent of maybe what people would like to have or what I wish we could afford, but basically it keeps the entire system intact and protects the elderly and keeps our pledges to them . . . . "

Stockman acknowledged that voting to support the cuts would be tough for many Republican senators planning reelection bids next year. "Yes, it is a very tough vote . . . ," he said, But all of them will have to look at the big picture. We can't keep this kind of growth, this kind of economic prosperity going -- that is very satisfactory to the American people and which they reaffirmed in the 1984 election -- through 1986 unless we get this budget under control."