Testifying on behalf of millions who could use emotional help, Rosalynn Carter quietly told a Senate subcommittee yesterday: "Everybody has a mental problem."

"All of us," said the First Lady, who has seen her own family touched by marital discord, can be affected by emotional upsets as the result of "marital problems... unemployment... drug abuse" or other events.

And asked by Sen. Claiborne Pell (D-R.I.) if she thinks Americans today face more stresses than they once did, she said: "I'm sure there are stresses. I'm sure that my children have more things to contend with than I had."

With her comments, the First Lady thus followed her own advice to "people who have had a mental health problem" to "speak out," because it helps other people with problems feel "it's all right," rather than feel a shameful stigma.

Her son Chip and daughter-in-law Caron announced last November that they were separating and Mrs. Carter had said little about her feelings until yesterday's admissions.

Making the first appearance by a First Lady before a congressional body since Eleanor Roosevelt, Mrs. Carter spoke softly and feelingly for the emotionally ill she herself has seen and touched in her years working for them -- and in harder and louder tones on the need for more money to attack the problem.

Senate health subcommittee Chairman Edward M. Kennedy, agreeing fully with her aims, said that federal "funding for basic research has grown impressively" since the early 1960s.

It was then, the Massachusetts Democrat noted, that his brother, President John F. Kennedy, "called attention to the non-system of mental health care."

"I have to take issue with you, Senator," on dollars for research and prevention, Mrs. Carter replied. Unitl 1967, she said, research funds did increase, but since then they have been cut in half in real dollars by inflation.

Then she argued for the recommendations of the President's Commission on Mental Health, of which she was de facto head.

She also gave the subcommittee a statement strongly defending the additional monies allotted mental health in her husband's otherwise austere fiscal 1980 budget, which either cuts or holds level most other health programs.

Mental health programs would get $633 million in 1980, up $59 million or 10.2 percent, from the 1979 figure. With money already added to the 1979 budget, "this will make a total of more than $100 million in new funds as a result" of the influence of Mrs. Carter's commission, a federal health official reported.

No senator asked her how she felt about mental health getting one of the few sizeable increases among all federal programs.

But she said in her prepared statement, in a part she did not read or touch on: "People often ask me how I justify pressing for more funds for mental health when there are so many problems facing the nation. It is easy for me to remind them that our mental health problems are serious -- and that we have endured years of neglect of the mentally ill -- and that no other problem facing society touches so many families or leaves them so vulnerable."

Among the mental health commission's 117 recommendations, she saw three "main priorities":

Broadening the national network of community mental health centers -- local treatment units -- into a "community mental health system" with more capacity to help underserved populations. This includes the chronically ill who are too often "dumped" out of mental hospitals into communities unprepared to support them.

Developing new ways to finance mental care, including private and public insurance coverage.

Research into the still too little understood causes of mental illness and retardation, and possible treatments.