Lady Bird Johnson, speaking at the winter commencement of George Washington University, yesterday denounced any proposals to cut federal aid to college students as a mistaken retreat from the promise first made by her husband, President Johnson, that all Americans have a "right" to higher education if they can "absorb" it.

The former first lady did not specifically mention the 25 percent cut in federal spending on student grants and loans proposed in President Reagan's budget for the 1987 fiscal year. But she said that breaking "the promise of . . . expanded educational opportunities . . . would be to put our future in peril."

Although she said there should be no "contest" between spending on education and defense, which the Reagan administration seeks to increase, Johnson declared: "Perhaps the time has come when we must redefine the requirements of national defense and recognize that it includes not only hardware but other ingredients as well, just as critical -- education being chief among them."

Johnson, 73, walked with a cane and delivered her speech while seated at a table in the university's Smith Center, explaining that she had "a temporary bad knee" because of an accident two weeks ago. She was hospitalized for tests for five days after a fall and a fainting spell.

Yesterday she said she had been staying at the Northern Virginia house of her daughter, Lynda Bird, and son-in-law, former Virginia governor Charles Robb, since Thursday. The Robbs were among about 5,000 people attending yesterday's ceremony, where Johnson received an honorary doctor of public service degree. About 850 graduates were given diplomas.

Lynda Bird Robb was a student at George Washington University while her father was president during the 1960s. She later graduated from the University of Texas.

In its budget proposals released this month, the Reagan administration said student aid cutbacks were necessary to reduce the federal budget deficit and said the aid should be aimed at the disadvantaged.

Johnson acknowledged that there are "limitations on federal spending that once we did not recognize," referring to the major growth in government programs under her husband's Great Society. But she said the country "can . . . afford the educational promises that we made."

Among those applauding Johnson loudly were Mary Hatwood Futrell, president of the National Education Association, and Rep. Michael D. Barnes (D-Md.), both of whom received distinguished alumni achievement awards.