An estimated 3 million households would lose all or part of their benefits under the budget cuts and other changes President Reagan has proposed in the Social Security system, according to program statistics and budget documents.

These figures emerged yesterday as openly skeptical Democrats on the House Social Security subcommittee challenged Reagan budget director David A. Stockman to back up claims that proposed cuts in social programs would not hurt the truly needy.

The administration seeks to save $4 billion from Social Security in fiscal 1982 by phasing out student benefits, cutting minimum and burial benefits and making it harder to qualify for disability assistance.

Yet subcommittee member Andrew Jacobs Jr. (D-Ind.) charged -- and Stockman acknowledged -- that at the same time the administration intends to create a new benefit for people who are not fully retired and who, according to figures obtained by The Washington Post, are largely well-to-do.

The new benefit, Jacobs said, would result from Reagan's proposal during last year's election campaign, which Stockman made clear is still operative, to repeal the $5,500 limit on the amount a Social Security beneficiary can earn without reduction of retirement benefits.

Statistics obtained later show that the phaseout of student benefits would affect 772,000, the reduction of the minimum about 1.5 million people, the disability changes 55,000 and the loss of burial benefits about 700,000.

At the same time, the president's plan to wipe out the earnings limit would mean increased benefits for 1.1 million people, totaling some $7 billion to $8 billion a year, and two-thirds of these new benefits would go to people earning more than $17,500.

Rep. James M. Shannon (D-Mass.) told Stockman he did not believe that the administration has any real information on how some of the proposed cuts would affect the poor, and he said to reporters after the hearing, "This baloney that there will not be needy people hurt by these changes, it's just baloney."

While Stockman was defending proposed Social Security cuts -- and also saying he opposes efforts to give beneficiaries less than full cost-of-living allowances each year -- Secretary of Labor Raymond J. Donovan sought to reassure more than 300,000 holders of public service jobs that the government would help them find work in the private sector if Congress does as Reagan wants and phases out their public service slots to save $3.6 billion.

"We will do everything possible to move them into other jobs quickly," said Donovan in a statement. Among steps Donovan said would be taken: setting aside $245 million to cover unemployment compensation for those unable to find jobs quickly; asking the Chamber of Commerce, National Governors Associati Association and various other groups to make special efforts to find jobs for those displaced; trying to find displaced workers other slots under what would remain of the Comprehensive Employment and Training Act programs.

All over Capitol Hill yesterday there were clashes and debates over Reagan's plan to cut the budget for nondefense items by $45 billion in fiscal 1982:

House Majority Leader Jim Wright (D-Tex.) estimated in an interview that Reagan would get $25 billion to $30 billion of his requested cuts and wouldn't succeed in getting the three-year, 30 percent tax cut he is seeking. Earlier Wright had sent a nine-page letter to House Democrats asking them not to rubber-stamp Reagan's proposals.

Reps. Thomas Downey (D-N.Y.) and Carl Pursell (R-Mich.), speaking for the congressional Northeast-Midwest Coalition, charged that the Reagan budget will hasten the decline of those two regions by cutting funds that help them.

They said that from 1975 to 1979 the Frost Belt states sent $165 billion more in taxes to the U.S. government than they got back in federal spending, while the Sun Belt was getting back $112 billion more than it paid in.

The Coalition for Health Funding told a House budget unit that "this hasty cutting of federal support" in some health programs would ultimately backfire and lead to more costly health insurance, higher hospital costs and higher health training costs; and the American Association of Retired Persons said proposed caps on Medicaid and other health-program reductions could tear a huge hole in the social "safety net" that the president says he is preserving.

Acting Chairman Stuart Statler of the Consumer product Safety Commission said cutting its budget would severely hamper its work, reducing information on injuries and enforcement of standards, and other witnesses said accidental deaths of children might greatly increase without the CPSC.

Amtrak chief Alan Boyd said that if the Reagan cuts go through, all passenger service outside the Northeast corridor would have to end, a development that Sen. Howard Cannon (D-Nev.) called "unacceptable," but Robert Blanchette, chief of the Federal Railway Administration, which regulates the railroads, disputed Boyd's assertions.

Stockman told the Senate Small Business Committee that the government cares more about businesses that can operate largely in the competitive market than those that need continued government help, and therefore cuts in small business assistance are justified.