Joe Washington can remember hoping when he was much younger that he would grow up to be big, maybe Jimmy Brown big.

"My hands got big, my feet got big but the rest of me didn't grow much more," he said today, laughing about an elusive dream of long ago.

Instead of size, Washington was blessed with quickness, enough quickness for a teamful of players. He gave up trying to run over people in grammar school. He found it much easier to dart by them while they were still trying to read his uniform number.

The Redskins haven't had Joe Washington's kind of quickness, the kind that can turn corners and slash through the middle on draw plays, since Mike Thomas was exiled to San Diego. An evena Thomas might not have been as quick.

For both the Redskins and the player, this marriage could not ahve happened at a better time. Rarely has a team in the NFL had a greater need for a fast back. And rarely has an athlete been more ready than Washington for a renewal of his football life.

The Redskins were tired of having end sweeps turn into four-yard losses, of defenses cheating to the inside because they knew no one could get outside. Washington was tired of his former employer, the Baltimore Colts, and a contract hassle that had lasted for two years without apparent progress.

Now Washington, at age 27, has a new Redskin contract and an offense that appears to have been invented for him. And Coach Joe Gibbs is staying up nights, doodling on his yellow pad, finding ways to utilize all of his new halfback's gifts.

"What we are going to ask him to do, things like traps and draws and sweeps and coming out of the backfield on passes, they are the things he does the best," said Don Breaux, backfield coach. "Hes, this is an offense that should benefit Washington."

And what does Washingvton, the serious son of a high school football coach, envision?

I would love to get 800 yards rushing and 800 yeards receiving," he said. "I think i'd be contributing a lot that way."

If he could meet those goals (the team combined yardage record is 1,689 by Larry Brown), Gibbs would be ecstatic. It would mean Washington would carry the ball about 225 times and catch 70 or more passes. And every time he touches the ball, he is a threat to break off a big play, another rare occurrence recently for the Redskins.

The Redskin backfield has been blessed with a depth and versatility it has lacked in recent years. Washington, John Riggins, Wilbur Jackson and Terry Metcalf all have rushed for at least 790 yards in a season. Washington, Jackson, Mtcalf and Clarence Harmon all have caught at least 50 passes in a season. But Washington remains the vital cog, the man with the much-sought-after jets.

"He's not the fastest guy in the world," said Mike Allman, the Redskin player personnel director, who scouted Washington in college. "But he's so darn quick, he just gets by you before you know it. And once that happens, he doesn't get caught from behind that many times."

Washington is a darter, one of those runners who seems to be going in three different directions at the same time. He has, according to Allman, "the greatest lateral quickness i've ever seen, with the exception of Gale Sayers. Once I saw him leap a pile of tacklers, land on one foot and, instead of going forward, jump to the side and take off. You just don't see that happen very often."

He also is reaching full maturity. He's five pounds heavier than last year (up to a bulging 184) and stronger. And he says he's never felt quicker or faster.

"This is the start of a new career for me," he said. "After all the contract hassle in Baltimore, I feel like a big burden has been lifted off my shoulders. The little things were getting to me. I needed new faces. This is where I should be."

Six years ago, Washington was the fourth man picked in the draft, by San Diego, after a dreamlike college career at Oklahoma. His hand-painted silver shoes slashed through the conference record book (he averaged 6.1 yards a carry) and the Sooners lost only two games in his four years. One of the most exciting punt returners in college history, he had a string of game-breaking runs that won a national title for his school his senior year.

But in an exhibition game in his rookie pro season, in of all places, the University of Oklahoma stadium, he hurt his knee. He sat out the schedule. It was the first time in an already fabled career -- he is a high school legend in Texas -- that he had been hurt. And from then on, there was a question around the league whether he was big enough to withstand NFL punishment.

His performance in Baltimore, however, should have dispeeled any doubt about either his durability or his ability to play in the NFL. He led the league with 82 receptions in 1979, when he made the Pro Bowl, and he gained 956 rushing yards in 1978 and 884 in 1979. Only in 1980, when he shared time with Curtis Dickey, did his statistics decline.

"There's no better back in the NFL for running pass routes," Breaux said. "Most can do the short ones, but he can do them right when he extends them 30 or 35 yards. And how would you like to be a linebacker out in the flat, trying to stop him one on one?"

The soft-spoken Washington, a banker in the offseason, knows the value of working on those linebackers. He'd like nothing better than to make a career from swing passes. Darrell Royal, the former Texas coach, spent four long years trying to defend against just such plays. "A guy like Washington," Royal said, "makes you awfully disappointed in your tackling."