For young artists, to perform at the White House is an honor, a privilege and a special experience in their lives. If they happen to be dance artists, as was the case yesterday afternoon in the "In Performance at the White House" series, then it is also something of an obstacle course.

The East Room, the site of these events, is, of course, a very handsome salon, but its matchbox stage--lacking many theatrical amenities, booming with hollow sound and hemmed in from above by massive chandeliers--is not your ideal locus for dance. It's a great tribute to the pluck and professionalism of yesterday's cast that they coped so beautifully with these limitations, and served up a nicely balanced show that may well have looked better on television, where it was seen locally on Channel 26 last night (to be repeated Saturday evening) than it did in the flesh.

Yesterday's performance was the third in a series of four under the auspices of President and Mrs. Reagan, who were present for the occasion, along with series mistress of ceremonies Beverly Sills and special host Gene Kelly, on hand to introduce the dancers. The program, produced jointly by WETA of Washington and WNET of New York, offered samplings of modern dance, classical ballet and tap dancing, as performed by members of the Martha Graham Dance Company, the San Francisco Ballet and Greg Burge of the original "Sophisticated Ladies" cast.

In the opening round of introductions, Nancy Reagan observed that "America has become the dance center of the world," adding that she would be saying this "even if my own son wasn't an up-and-coming dancer"--a reference to Ron Reagan, who is a member of the Joffrey II troupe.

The program proper got started with Christine Dakin and Donlin Foreman of the Graham troupe dancing a duet from "Appalachian Spring," as the pioneering couple originally performed by Graham and Erick Hawkins in 1944. Closer to the earthy, soulful spirit of the Graham troupe's earlier incarnations was a performance of the wrenching solo "Lamentation" (1930) by one of the company's newest members, Joyce Herring, who has touches of Graham's own tragic urgency as we know it from the past. The Graham sampler concluded with a duet from the slow movement of "Acts of Light"--premiered at the Kennedy Center last year--ardently danced by Dakin and Foreman.

Evelyn Cisneros, Linda Montaner, David McNaughton and Kirk Peterson of the San Francisco Ballet next presented "Quattro a Verdi," by troupe director Michael Smuin. It's an old-fashioned barn burner with solos for each dancer, a pas de trois featuring Montaner and an adagio for Cisneros and Peterson. The dancing was sparkling, the men in particular displaying virtuoso fireworks of eye-popping brilliance. Greg Burge, introduced by Kelly from the stage, danced the "It Don't Mean a Thing (If it ain't got that swing)" number from "Ladies" with syncopated razzle-dazzle. And for a close, Cisneros and Peterson gave a snazzy premiere to a Smuin tap duet set to Stravinsky's "Ragtime," with James Lees at the on-stage piano.

After President Reagan thanked the artists, he and Mrs. Reagan, Sills, Kelly and the dancers chatted with invited guests at a buffet reception. Graham, 87, was there, regal as ever, wearing the presidential Medal of Freedom she received in 1976. And dancers Cisneros and Peterson offered an explanation for the performers' aplomb: "We rehearsed in an even smaller space, so when we got to the real thing, it felt luxurious by comparison."