SIOUX FALLS, S.D., FEB. 19 -- The morning after Tuesday's New Hampshire primary, Rep. Richard A. Gephardt (D-Mo.) got up at 6 and flew here looking for votes. "This is a pivotal state . . . ," he told a gathering of senior citizens. "I want you to know how important it is."

That may be no more than typical campaign hyperbole, but in a fight as muddled as this year's Democratic nomination contest, even states like South Dakota, which has 15 Democratic delegates and holds its primary on Tuesday, can help.

On the Republican side, Senate Minority Leader Robert J. Dole (Kan.) is the heavy favorite because of his midwestern roots.

On the Democratic side, Massachusetts Gov. Michael S. Dukakis, on the basis of a strong organization, is the favorite here, but the polls tell a contradictory story. One shows Dukakis well ahead, another shows him tied with Gephardt, while others show that a large number of voters haven't made up their minds.

A Gephardt poll of 400 voters Wednesday night showed Dukakis ahead, 39 percent to 28 percent. But Gephardt's strategists contend that Dukakis' support is soft. "People are still driven by name recognition," said one Gephardt adviser. "Dukakis got started earlier here and did a lot of advertising out of Sioux Falls during the Iowa campaign."

Gephardt got a boost this week when Sen. Tom A. Daschle and former governor Harvey Wollman endorsed him, but advisers to the two campaigns disagreed on how much that would aid his fortunes.

"The endorsement gave Gephardt a big boost," said Fritz Weicking, Dukakis' state campaign manager, "but it didn't take support from us as our previous poll indicated it would."

Gephardt is plagued by organizational problems, however. Although he has about the same number of full-time workers here as Dukakis -- about 40 or 50 each -- Gephardt's army appears to be one without a general whereas Dukakis' organization is considered excellent.

"I was at a business luncheon recently where at least half the people there had been called by Dukakis' organization," said one political observer.

"He's the only one who has the organization to turn his people out. And people in this state don't mind voting for a slick eastern liberal in a three-piece suit. They voted for Ted Kennedy in 1980, and they think Dukakis looks presidential. The farmers like him. He was the only one who showed up at the state fair last fall to talk to them, and that counts for a lot in this state."

South Dakota will send one of the smallest delegations to the Democratic convention this summer, but a good showing here and in the Minnesota caucuses, which also are next Tuesday, can realize dividends down the line.

Victory would give Gephardt something of a boost going into his formidable task of competing in the southern regional "Super Tuesday" primary on March 8. Victory for Dukakis would embellish his New Hampshire victory.

Sen. Albert Gore Jr. of Tennessee, who has based his candidacy in the South and hasn't paid much public attention to South Dakota, is uneasily regarded as a sleeper by his rivals. He has made a near-saturation purchase of television time and will campaign here Tuesday in the hope of giving his Super Tuesday campaign a boost by finishing third.

"He thinks this is a state where he could finish third," said Steve Raabe, Gore's state campaign manager. "He won the debate here on Jan. 29 because he listened to Lad Herseth {the 1986 Democratic gubernatorial candidate} and was the only one who talked about South Dakota issues."

Sen. Paul Simon (D-Ill.), who belatedly discovered the importance of South Dakota after his third-place finish in New Hampshire, is making a last-minute campaign blitz and saturation television purchase here this weekend. He announced on Wednesday that he needs to win here or in Minnesota on Tuesday to keep his campaign alive but announced yesterday that he is in to stay regardless.

Democratic candidates' tracking polls show support for Jesse L. Jackson hovering just below 10 percent, about equal to his Iowa showing.

The Republican primary, in which 18 delegates are at stake, has become a no-contest as everyone but Dole is by-passing South Dakota to concentrate on the South. Neither Bush nor Pat Robertson will campaign here, while Rep. Jack Kemp (N.Y.) is still trying to decided whether to do an event on Monday.

"With the magnitude of our Iowa loss, it was a foregone conclusion that we weren't competitive in South Dakota," said a Bush strategist. "We're going with a volunteer operation and will try to get out with a handful of delegates." Robertson is not expected to do well because this is a northern primary state, but as elsewhere he is an unknown factor. In just four appearances in the state, he has drawn crowds totaling 3,000.