The White House mounted a full-court press yesterday to rebut most of a CBS News television documentary, "People Like Us," which blamed hardships faced in four cases by the poor or disabled on President Reagan's budget cuts.

"Frankly this one was below the belt," said White House Communications Director David R. Gergen, who orchestrated a day-long series of briefings by administration spokesmen to challenge the accuracy of elements of the report and to question the "fairness" of airing it without giving administration spokesmen an opportunity to respond.

The documentary comes as Americans increasingly are questioning the fairness of Reagan's cuts in social spending and are indicating in public opinion polls a deep dissatisfaction with the way he is handling his job. Both are matters of deep concern to the White House.

Yesterday, Gergen asked that CBS give the White House 30 minutes of network time to broadcast a film that the White House would prepare and finance through private sources. CBS president Van Gordon Sauter denied the request, noting the "extensive coverage" it "has and will continue to provide to administration viewpoints."

In the hour-long documentary Wednesday night, narrator Bill Moy-ers had asserted that Reagan and Congress, while sparing federal subsidies for middle-class Americans and big corporations, had let the burden of budget cuts fall on the poorest and least politically powerful Americans.

The four persons focused on in the program were an Ohio man with cerebral palsy who had been dropped from disability rolls; a New Jersey woman forced to quit her job and go back on welfare so her ailing son would be eligible for government medical benefits; a 13-year-old Wisconsin girl, who suffered two strokes, and a Milwaukee priest who supervises a food program for the poor.

"The burden falls most heavily on the poor," Moyers said in concluding the documentary, "and some of the truly needy are truly hurting . . . . For all the fraud and waste, for all their inefficiencies, these programs are a life-support system for the poor. For many, we are pulling the plug."

As part of their campaign to discredit those conclusions, administration spokesmen issued a fact sheet disputing that the plight of the disabled man, the woman and the girl had resulted from budget cuts. They did not challenge the priest's case.

"I don't think that one could have watched that show . . . without feeling a powerful sensitivity for the individuals involved . . . ," Gergen said. "Those individuals clearly had difficulties in their lives.

"What we have problems dealing with is a story which lays all of the problems of that sort and all of the issues that have been with this country for a long time, the fact that people suffer in this country . . . the fact that people are hungry in this country . . . the fact that there are poor people in this country . . . on Ronald Reagan's doorstep."

At a later briefing, Assistant Health and Human Services Secretary Robert Rubin described examples cited by Moyers as misleading. "We are committed to preserving the social safety net," Rubin said.

Rubin released a fact sheet challenging three of the cases, contending:

That the administration had not cut federal payments to states for visiting nurses as alleged in the documentary's segment about Carrie Dixon, the comatose Wisconsin girl whose mother reluctantly institutionalized her because she feared she could not continue to care for the child at home.

Rubin said the administration is working on a policy to encourage more home care. Officials in Wisconsin agreed.

CBS "picked the wrong case," said Joe Scislowicz, information officer for the Wisconsin Department of Health and Social Services. Wisconsin officials said the state had recommended to Dixon's mother that she institutionalize her daughter only because they felt it was too much of a burden on the family to continue home care.

That cerebral palsy victim Larry Ham apparently waited until April to appeal cutoff of his disability benefits, although he had been warned in December that they would be stopped.

Rubin defended a nationwide step-up in investigating persons such as Ham who receive Social Security disability benefits, indicating that it has for the most part rooted out only those who are ineligible.

That view contradicts findings by several private groups studying the problem and by many congressmen who have been hearing horror stories from constituents who have serious medical problems and whose benefits were suddenly halted.

That federal budget cuts were only in part responsible for creating a situation that forced Frances Dorta, the divorced New Jersey mother of three, to quit her job and go on welfare to remain eligible for Medicaid benefits to pay for her son's operation.

Quitting her job was "probably an appropriate response," Rubin said, and proof that the social safety net is working.

Asked if the administration believes that working mothers, as a matter of policy, ought to be forced to leave jobs and go on welfare to receive medical benefits, Rubin said, "Absolutely not," conceding that her situation was not "ideal."

Administration spokesmen did not deal with the segment on a voluntary program at St. Benedict's Church in Milwaukee where food is provided for persons whose food stamps have been cut off or reduced. Moyers had asked the Rev. Steve Gliko about Reagan's assertion that the administration is caring for the truly needy.

"What's your response to that?" Moyers asked.

"Simply the fact that the American citizen who can say that is blind!" Gliko said.

Preliminary overnight ratings indicated that the documentary was seen by very small audiences--12 percent in Chicago, 10 percent in New York and 9 percent in Los Angeles. That prompted some White House advisers to question whether their rebuttal campaign would draw even more attention to the program.

Aides would not characterize the president's views but said he approved the decision to make the rebuttal.

The Republican Senate Policy Committee showed the documentary to GOP staff aides yesterday afternoon and provided them a list of the show's corporate sponsors.

Gergen said he had no knowledge of any White House involvement with that effort.