DES MOINES, FEB. 6 -- The longest Iowa siege ever -- collectively, the Democratic presidential candidates have campaigned a record 634 days in this state -- heads toward its Monday night climax with Rep. Richard A. Gephardt (D-Mo.) leading in the polls over Sen. Paul Simon (D-Ill.) and Massachusetts Gov. Michael S. Dukakis, while four others are well back in the pack.

The winner of this first Democratic contest will catapult off to New Hampshire the morning after with a tiny cache of delegates and a gigantic media boost in a field that has been without a true front-runner since last May, when former Colorado senator Gary Hart temporarily abandoned the race. A total of 58 Democratic delegates are at stake.

The Des Moines Register will publish a poll Sunday showing Gephardt at 25 percent; Simon at 19 percent; Dukakis at 15 percent; former Arizona governor Bruce Babbitt and Jesse L. Jackson each at 9 percent; Hart at 7 percent; Sen. Albert Gore Jr. (Tenn.) at one percent; with 15 percent undecided. The poll of 612 likely Democratic caucus-goers was taken from Jan. 25 through Feb. 3. Other public and private polls taken this week show the top three candidates bunched more closely.

In order to convert his poll numbers into delegate strength Monday night, Gephardt needs a heavy turnout from farmers and blue-collar workers to whom his tough trade talk and anti-establishment appeals have been targeted, particularly in his now-famous television blitz. {Details, Page A14.}

Many are not habitual caucus-goers. "Turnout is the whole game for us," said Gephardt's campaign manager, William Carrick. "The more you shrink the universe down, the better the others are likely to do."

Democratic State Chairman Bonnie J. Campbell is projecting a record turnout of 125,000 at the 2,487 neighborhood caucus sites around the state. That would be slightly more than 20 percent of the state's 570,000 Democrats. The previous record turnout was an estimated 100,000 in 1980.

"This is the most intensive race I've ever seen here," Campbell said. "The candidates have been at it longer, they're better organized, and everyone realizes it's very close." (Since Iowa became the state for the nation's first caucuses in 1972, the first- and second-place Democratic finishers have never been within 10 points of one another.)

Others are less certain about a high turnout, noting the absence of powerful personalities, overriding issues or even much candidate sparring in the closing weeks. "It's almost like a basketball game that went into a stall at the end," said Gephardt pollster Ed Reilly. "It's a very late-breaking, very soft and not very excited electorate," said analyst Robert Beckel, Walter F. Mondale's 1984 campaign manager who returned this week as part of the record 3,000-member media invasion.

Iowa's function at the head of the calendar has been to winnow the field. While each candidate has a different objective here, the most critical confrontation is between Gephardt and his fellow midwesterner, Simon. They are in a struggle that could doom the loser's campaign. Very likely, each must win -- or at least defeat the other -- in order to be competitive the following week in New Hampshire. Each has invested massively in this neighboring state -- Gephardt has campaigned here 148 days; Simon has 1,265 volunteers knocking on 30,000 doors this weekend, and was the poll leader for much of last fall.

Dukakis, on the other hand, does not face a must-win situation. He's already "winnowed in" by his New Hampshire base (estimated at about 35 percent of the Democratic vote). But a lagging third-place finish in Iowa -- a state where he has campaigned 82 days and assembled what many regard as the best field operation -- would expose him to charges that his technocratic image does not travel well. "The question for Dukakis is whether he can reach people's hearts as well as their heads," said Simon campaign manager Brian Lunde. "Especially in a caucus state, people have to feel good about you."

Simon has been running the most "feel good" campaign of the seven, focusing on soft appeals to character, consistency and trust rather than on issues. He campaign was perceived to be flagging until last Sunday, when he got the editorial endorsement of the Register, the dominant state newspaper. "The guy with the last momentum wins," said Paul Maslin, Simon's pollster, "and we have it. The Hyundai has run out of gas," a reference to a now-famous Gephardt's ad threatening tariffs that would raise the cost of that car to $48,000 unless South Korea opens its market.

As for the others in the field:Hart was at 65 percent in the Des Moines Register poll before he dropped out of the race last May. He was at roughly half that when he returned in December, and now is at 7 percent. The rally cry in the five-minute commercials he began airing last week is "Let the people decide." Babbitt needs to break into the top three. And he is hoping that the contrast he has drawn between his "honesty" in calling for tax increases and domestic spending cuts on a "needs-tested" basis, and his opponents' "flim-flam" solutions to the budget deficit will do the trick. But party activists around the state detect little momentum for him, and rival campaigns say his stinging attacks have backfired. Some speculate he could finish fifth. Jackson is out to show that a black preacher and civil rights activist from South Carolina, via Chicago, can make a splash in 98.5 percent white Iowa. His goal is to score in double digits. He has endorsements from farm groups and the state teamsters union, and yesterday was jointly endorsed (with Simon) by Star PAC, a prominent peace group. He is no longer campaigning to change the party's rules (as he did in 1984) and has built up good will among party regulars. Since the other campaigns do not perceive him as an immediate threat, he is more likely than anyone else to get help from rivals in caucuses where his supporters fail to make the 15 percent viability threshold. (Under party rules, candidates with less than 15 percent in a given caucus site do not get any delegates.) Gore started campaigning here last summer but pulled out in the fall, claiming the process was distorted by special interest groups. His high-risk strategy is to save his resources until "Super Tuesday," March 8, when 20 states will hold primaries or caucuses. But for now, he is heading into his dry season.