CBS News yesterday defended its documentary "People Like Us" against White House criticism that it contained errors and had misstated the impact of President Reagan's budget cuts on three poor persons.

The network said that it had again contacted the people profiled in the documentary televised Wednesday night and that they affirmed that their plight had been accurately portrayed.

"The statements of the Reagan administration . . . criticizing the accuracy of our broadcast, are incorrect," CBS News said in a low-key, five-page, point-by-point rebuttal of the administration's charges. The network failed, however, to clear up one of the administration's specific objections to the documentary.

Extremely sensitive to growing perceptions that the Reagan economic program is hurting the poor, the White House had orchestrated several briefings for reporters to dispute the documentary's findings and to complain about CBS' refusal to include an administration response in the program.

White House communications director David R. Gergen, in a free-swinging assault on the network, charged that CBS had hit "below the belt."

"People Like Us" told of problems faced by an Ohio man with cerebral palsy who had been dropped from Social Security disability rolls, a New Jersey woman who quit her job and went 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 runs a food program for the poor.

The administration had contended that the Ohioan's disability benefits were stopped because he did not appeal the cutoff until five months after being notified of it.

CBS said that less than a week after the notification the man's lawyer called Social Security and later followed up with other calls and letters. CBS said the man's file had been mislaid for 2 1/2 months by the local Social Security office.

CBS disputed the administration's contention that the social "safety net" had worked for the New Jersey woman because her return to welfare had enabled her son to qualify for medical benefits and get the operation he needed.

Robert Rubin, assistant health and human services secretary, had contended that once the operation was completed the mother could return to work. CBS said Rubin's response ignored the fact that New Jersey's unemployment rate last month was 8.8 percent and that it was far from certain that the woman could regain her job.

CBS' defense of its report on the 13-year-old was that the documentary had stated only that the girl's mother institutionalized her because she was fearful about cuts in federally aided visiting nurses programs.

The network acknowledged yesterday that the nurses are still visiting. But it cited a memo by the Visiting Nurse Association of Milwaukee on the effect of spending cuts Reagan has proposed for fiscal 1983 in supporting its contention that the mother's fear "was understandable."

But, in an interview, a CBS official said that the memo had been written in March, two months after the mother institutionalized her daughter, and that the proposed cuts would probably mean the girl's family had to pay $3 a week to continue the nurse's visits.

Wisconsin officials said Thursday that the family receives $337 a month in benefits for the girl. Referring to that case, Joe Scislowicz, information officer for the Wisconsin Department of Health and Human Services, said CBS "picked the wrong case."

The administration had not contested the documentary's report about a Milwaukee priest who said his voluntary program providing food for those whose food stamps have been cut off or reduced had been dealing with increasing numbers of people recently.