Alfred E. Smith ran for president in 1928, only to lose to a man with the slogan: "It takes two Smiths to make a cough drop, but only one Hoover to sweep the country."

Tough town, Washington. Not much on politicians named Smith.

Fifty-three years later, there still hasn't been a Smith in the White House. But up on Capitol Hill, it's a different story. The voters last fall had a change of heart and now there are five Smiths in the House, the most in at least 20 years.

Not since Jimmy Stewart got off the train at Union Station in Frank Capra's 1939 classic, "Mr. Smith Goes to Washington," has Mr. Smith come to Washington in such force.

Is it a message from the electorate? The dawn of a dynasty?

"Well, the mail gets mixed up," says Neal Smith, a 12-term Iowa Democrat. "There haven't usually been so many Smiths."

He's right. Besides Smith (Neal) and Smith (Virginia, a fourth-term Republican from Nebraska), there now are three fresh Republicans: Albert Lee Smith Jr. of Alabama, Denny Smith of Oregon and Christopher H. Smith of New Jersey.

And there's Reagan's attorney general, William French Smith, who was too busy to comment on the Smith landslide. "But when he flew out here from Los Angeles the last time, there were six Smiths on the plane," said his colleague helpfully.

James H. Smith Jr. of Camp Hill, Pa., founder and president of the 1,060-member Jim Smith society, says he doubts these recent gains mark a trend. But he has a dream.

"Personally, I'd like to see a Jim Smith running for governor in every state," he says. "Then on Election Night, David Brinkley could raise his eyebrows and say, 'Well, Jim Smith's trailing in Michigan, but he's ahead in Texas."

For the Smiths in Washington, the dream is now. "I'll remember the swearing-in for the rest of my life," says Chris Smith, 27, the youngest member of the Smith delegation. "I looked up from the floor of the House and there was my family waving from the third-row gallery."

There is fierce pride in a Smith who makes it to the nation's capital. It means he's survived what a writer once dubbed "the ordeal of Smith." The motel hassles ("Sure your name's Smith, buddy"), the cough-drop jokes ("Are you Trade or Mark?"), the struggle to stand out in the crowd.

Denny Smith, who unseated Rep. Al Ullman, worried about name recognition in his campaign. Then somebody had a bright idea: a committee called Smiths for Smith. "It wasn't that many people," says the victorious congressman, "but it got great press."

With the newcomers, Smiths account for about one percent of the House membership, meaning they now reflect the general population.

There are about two million Smiths in America, roughly the same percentage. It is the most common name in the country (numerically, of course), and although there have been no snafus in the House roll call yet, the Smiths are prepared by experience to expect confusion.

Albert Lee Smith Jr. remembers leaving the Navy after two years in the 1950s. On his way back to Alabama, he stopped at the Navy Department in Washington to check his service record.

"I was looking through it and I discovered I'd been awarded the bronze star for heroism in the Battle of the Philippine Sea. That was in 1943 when I was 12." He says he asked a flustered clerk for the medal. "They discovered there were eight Lt. j.g. Albert L. Smith Jrs. on file. They'd given me the wrong one."

As a Smith Jr., the future congressman was raised to look out for this kind of trouble. "When I was growing up, my mother would announce phone calls for my father, 'Albert Lee,' he says, imitating her deep voice. "When it was for me, she said, 'Albert Lee ,'" in a high-pitched squeak.

(It was not immediately known how Smith's 12-year-old son, Albert Lee Smith, III, deals with the problem.)

Identical full names can spell trouble.Neal Smith of Iowa recalls that a man of the same name in his hometown had a bad credit rating. Rep. Smith had trouble cashing checks.

The name is so pervasive it has its own literature. A Chicago lawyer named Elsdon C. Smith, author of "The Story of Our Names," something of a bible on the subject, says Smith derives almost entirely -- but not exclusively -- from the occupation of smithy. Every village had one. It also has roots in the jousting fields near London, which were said to be smeeth , as opposed to bumpy.

In "People Named Smith," author H. Allen Smith notes gleefully that Mark Twain dedicated his first book, "The Celebrated Jumping Frog," to John Smith, on the theory that the man to whom a book is dedicated always buys a copy. "If this prove true in the present instance," Twain wrote, "a princely affluence is about to burst upon -- The Author ."

The name has even given rise to protective associations formed in self-defense. Such as the National Society to Discourage Use of the Name Smith for Purposes of Hypothetical Illustration (or the NSDUNSPHI if you're rushed). According to Elsdon Smith, it is the duty of members to present their membership cards when they hear anyone refer to an imaginary character as Smith.

One fictional character, in a novel by P. G. Wodehouse, changed his name to Psmith because there were so many Smiths in the world. "The p, I should add for your guidance, is silent," he says.

The popularity of hyphenated names in Britain -- Heathcote-Smith, Broke-Smith -- once moved to Ogden Nash to write: In the phalanx of hy-Phenated Names !

(Have you ever observed That the name of Smith Is the oftenest hyphenated with ?)

President Smith or no, first ladies, of course, have infiltrated the White House. Abigail Smith Adams holds a record of sorts as wife of one president and mother of a second. Rosalynn Smith Carter spend a term there before the voters -- probably unaware of her heritage -- repudiated her husband.

One who speaks wistfully of his days as a Smith on White House duty is former Carter speechwriter Griffin Smith.

"Somebody sent me an article from The Miami Herald by a writer named Griffin Smith," he says. "I followed it up with a phone call. It was a woman." His dream was to invite her and a Rev. Griffin Smith he discovered in the Washington phone book to lunch one day in the White House mess, but time ran out and he never did.

Another story by Griffin Smith shows that Smiths need to be savvy at all times.

When he was a law student at the University of Texas, Smith was eager to take a popular constitutional law course taught by Charles Alan Wright. Wright, equally eager to keep the class to a manageable size, decreed that students whose names began with the letters D,E,F,S or Y could not enroll that semester.

Undaunted, Smith got a court order legally changing his name to Smith Griffin, went back to school and took the course.

During the semester, Smith's father, a Little Rock lawyer also named Griffin Smith, visited the campus and took his son along for an appointment with Wright. Throughout the interview, Prof. Wright -- apparently unaware of his student's legal tactics -- referred to the elder Smith as "Mr. Smith" and his son as "Mr. Griffin."

At the end of the term, Smith mentioned to a law school secretary that he had just gotten another court order returning himself to his rightful name.

"Well, don't let Wright see the order," advised the secretary, "until you see your grade."

He didn't.

On the Hill, meanwhile, the newly elected Smiths are settling in. But they'd better keep their guard up. A reporter named Smith recently telephoned the office of Rep. Chris Smith, saying he's like to speak to the congressman for a story about people named Smith.After several minutes spent on hold, a secretary came back on the line.

"That will be fine," she said brightly. "What was your name again?"