IN A DRAMATIC conclusion to his speech at the National Italian- American Foundation in Washington recently, President Reagan told the following story of an immigrant whose son realized the American dream:

"Decades and decades back, there was an Italian immigrant who came to America, and he started a family and worked hard and raised his children as best he could. One of his sons became a milkman.

"He, too, worked hard and married and had a family. And the milkman raised his children as he had been raised: They were taught to respect honesty, decency and hard work. They struggled to make ends meet. All of their money went to the education of their children. They put one son through college, and when he wanted to be a doctor, they put him through medical school. Because of their diligence, the son became a prominent surgeon in a great hospital.

One day that surgeon -- that son of a milkman -- saved the life of a president of the United States who had been shot.

"I know this story because I was the patient . . . ."

I know the story, too, because I was the doctor. As head of the trauma team at George Washington University Hospital I gave the President emergency treatment when they brought him there after he was shot in the chest in an assassination attempt on March 30, 1981. I still remember Reagan, despite the pain and stress, jokingly saying to the doctors, "I hope you're all Republicans."

I'm a Democrat, but I told him, "We're all Republicans today, Mr. President."

The president's remarks at the Italian American dinner accurately describe my family's path to success and correctly identify us as being among the millions of Italian Americans who have realized the American dream. Hard work, perservance, strong family units and confidence in self were the basic tools used to overcome the deficiencies inherent in their immigrant status. This cycle from immigrant to middle class to professional status has been repeated many times over the last 50 years.

My family and I are proud of the president's comments. Nevertheless there is another part of the story.

The government social programs enacted over the last 50 years -- and so frequently criticized by this President and his Administration -- have played a vital role in making this success possible. Although my father bore the brunt of the expense, I received low-interest government loans to help finance part of my medical school education. Many colleagues of mine received even greater government assistance in their education.

And my profession, stimulated by generous federal funding for biomedical research, has made unprecedented progress in diagnosis and treatment of disease in the last 30 years.

In contrast to the president, who feels that government programs make people so dependent that they lose initiative, I feel that these programs have enabled people with little resources to reach their full potential.

These programs are so numerous it would be impossible for me to mention them all. They range from Headstart to housing for the elderly. My parents enjoy a deserved retirement helped by Social Security, and my father has more than once benefited from the Medicare program.

Even the civil rights legislation of the 1960s, although primarily designed to guarantee equal rights for blacks, has aided Italian Americans and other ethnic and racial groups by making discrimination not only illegal but also socially unacceptable.

It is to be hoped that the president will recognize that millions of other Americans possess the same potential as Italian Americans. Some will make it on their own. Others will need help. I hope that the government will not stand on the commitment that has meant so much to me and my family.