Two presidential candidates of whom much was expected in 1988, Republican Jack Kemp and Democrat Richard Gephardt, are falling out of the race as the long precampaign year grinds to its end. They may yet recover, but the latest NBC poll shows Kemp running 36 points behind the leader in Iowa and 33 points back in New Hampshire; Gephardt, 11 points behind in Iowa and 46 behind in New Hampshire.

Each of their campaigns has had its specific problems, but they share a similar handicap: both are House members running uphill against a popular bias which says that the White House is off-limits to congressmen. It's a dumb prejudice, but it is powerful enough to have kept any sitting House member from gaining the presidency since James Garfield in 1880.

Rep. Morris K. Udall of Arizona recalled the other day that after he ran unsuccessfully for the Democratic presidential nomination in 1976, ''I had the experience of people calling me 'senator' when I came to town. They assumed that if you'd run for president, you must be a senator.''

Governors also enjoy an almost automatic cachet. Jimmy Carter and Ronald Reagan used the statehouse as a stepping-stone to the White House, and many Democrats are hankering for Mario Cuomo to follow their lead. But House members just don't make it.

Over the past five elections, the House has offered presidential candidates of considerable charm and ability, representing all varieties of thinking: conservative Republicans like Kemp, Phil Crane and the late John Ashbrook; progressive Republicans like Pete McCloskey and John Anderson; conservative Democrats like Wilbur Mills; moderates like Gephardt; and liberals like Udall and Shirley Chisholm. None has yet managed even to get nominated.

''I've never quite figured it out,'' Udall says, ''but House members don't have the mystique. There's an aura when a senator or a governor arrives. But a House member is just good old so-and-so.''

Udall has proved there is life after a presidential campaign. He occupies a position of considerable power as chairman of the House Interior Committee. His newly published memoir and assemblage of favorite political stories, ''Too Funny to Be President,'' is a delight. But it gripes him and other House members that the reputations people earn on the south side of the Capitol seemingly are not sufficient to sustain a successful presidential campaign.

Why not? It is not a question of effort. Udall all but exhausted himself in his long string of second-place finishes to Carter, and no one has worked harder or longer for the 1988 prize than Gephardt and Kemp. And they did it while remaining influential and effective legislators who earned the respect of their House colleagues. Gephardt is the elected chairman of the House Democratic Caucus, and Kemp held the counterpart position on the Republican side.

Both have had a major impact on legislation, larger than any of the Senate-based candidates except Bob Dole can boast. The landmark, across-the-board tax cut passed in 1981 was an idea which Kemp conceived and promoted tirelessly among his colleagues and across the country before Reagan came on board. Gephardt was a major architect of several health, trade, budget and tax bills -- including the 1986 tax-reform law.

Yet they are not accepted as being on a par with rivals who have other titles before their names, especially senator. Rep. Henry Hyde (R-Ill.), a Kemp supporter, thinks it is because ''the Senate is the smaller, more exclusive club,'' so ''being a member of the House -- or even in the House leadership -- is perceived as a lesser position.''

If that's the case, it's a misperception. It probably takes greater skills to be an effective House legislator, as Kemp and Gephardt have been, than to succeed in the Senate. The House is a larger, more diverse and more cumbersome body in which to work. Staff resources, while adequate, are not as lavish as in the Senate. A proposal's fate depends more on the elected official's own abilities, energies and alliances.

But most voters probably think of the House member as running a service agency, taking care of the pressing but usually parochial problems constituents may be having with the federal government. The service function is stressed in campaigns and public relations by most members of the House over their role as national legislators, while the reverse is the case for most senators. So the senator is seen as an ''awesome figure -- a wise man on Mt. Olympus,'' as Henry Hyde puts it, while the House member is just a Washington errand boy.

There are other differences, as well. Senate campaigns are more like presidential campaigns. They require raising and spending large sums of money, developing sophisticated television strategies, managing large staffs and dealing with diverse constituencies. Kemp and Gephardt probably hurt their chances to be president when they passed up opportunities to run for governor or senator in New York and Missouri.

But beyond all that, as Udall discovered to his chagrin in 1976, there's also a subtle, irrational bias against House members becoming president. It's a bias the country needs to overcome.