The Mondale-Hart 'full-court press' is on

The next eight days leading up to the Super Tuesday primaries present a super challenge to Walter Mondale and Gary Hart. But the challenge to each is different.

* Mr. Mondale, at all costs, must break the Hart momentum. Senator Hart's upset victory in New Hampshire already shows signs of snowballing into a powerful campaign that could become unstoppable.

* Senator Hart, despite lean finances, must demonstrate quickly that he is a nationwide contender. He must prove that New Hampshire was no fluke. Most important, Hart must show that he has appeal in the South, which will be crucial this year if the Democrats are to defeat President Reagan.

Both camps realize what's at stake. The Mondale team is using a strategy comparable to a ''full-court press'' in basketball. They are battling Hart every step of the way. They don't plan to give him a single free throw. That includes the little-publicized Maine caucuses, where Democrats are voting as this is written. It even includes Tuesday's unofficial ''beauty contest'' in Vermont, where voters will cast nonbinding ballots in the presidential race.

''We're in for a long, tough fight, and it could go right into the convention ,'' Mr. Mondale says.

The Mondale team needs to embarrass Hart very, very fast. At this stage, with the campaign in flux, public perceptions are all-important.

Mondale's planners would like to see the Hart campaign fall on its face early this week - if not in Maine, then in Vermont. A sharp setback might slow Hart's drive before it gets too much money, manpower, and momentum to control. Money is still Hart's most urgent problem.

Most important for Mondale, a quick Hart defeat could prevent the young Colorado senator from succeeding on Super Tuesday (March 13), when over 600 delegates will be at stake. That is nearly one-third of the delegates needed for the Democratic nomination. It once was expected to be the day that Mondale would finish off all his challengers and be assured of the nomination. That no longer appears likely.

The importance that Mondale puts on a quick Hart defeat could be seen during the past few days.

Within hours after New Hampshire, Mondale had dispatched his campaign manager , Robert Beckel, to Maine. At the same time, he ordered Michael Ford, his senior field director, to Vermont. Both Mondale and Hart made last-minute appearances in Maine in all-out bids for support.

Mondale's concerns are probably justified. Hart's campaign, which was broke, understaffed, and ignored by most of the media only a month ago, has ignited very much the way Jimmy Carter's did at this time in 1976.

The senator, who last month campaigned almost alone down the backroads of Iowa, today is followed by a growing army of reporters and cameramen. He's chartered his own Boeing 727 jet. His ramshackled national campaign offices over a movie theater in a poor section of Washington are suddenly bursting with activity. The five phone lines are constantly lighted, with some callers saying it takes over a hour to get through (20 more lines are to be installed today).

The explosive support for Hart is showing up across the map. Hart's Pennsylvania state coordinator, John Whitehurst, says he left his Philadelphia office for six hours on Thursday, and when he got back, there were 270 telephone messages waiting for him from people who wanted to volunteer or make contributions.

Here in Washington, the withdrawal from the race of Reubin Askew, Alan Cranston, and Ernest Hollings has prompted many of their supporters to rally for Hart.

Right after Hart's victory in New Hampshire, a number of analysts suggested that he would be unable to follow through, since he didn't have delegates on the ballots in some of the upcoming primaries. In Florida, for example, he had full slates of delegates in only 6 of 19 congressional districts.

Michael Levy, Hart's delegate counter, says concerns have subsided as other candidates have withdrawn.

It now seems likely that many delegates once pledged to Mr. Askew, Senator Hollings, and Senator Cranston will switch their allegiance, thereby making it possible for Hart to have full or nearly full slates in key states, Mr. Levy says.

For example, as we spoke in Levy's office, the telephone rang with a call from a man who was on the ballot as a Reubin Askew delegate in Illinois. The man said he represented a bloc of 16 Askew delegates who wanted to back Hart now that their man had pulled out.

In other states, the laws have loopholes that will allow Hart or anyone else to file their list of delegates after the vote. That's the case, for example, in Massachusetts and in New York.

With such technical problems apparently under control, Hart's strategists are turning their attention to the crucial political phenomenon known as momentum, or ''Big Mo.'' It is said that if Big Mo is on your side, that's the most important political ally one can have.

Prior to Super Tuesday, the Hart people are hoping to keep the momentum going by coming in no worse than second in the voting in Maine, Vermont, and the Wyoming caucuses on Saturday.

They hope to win at least one of them.

Then comes Super Tuesday. That consists of three major groups of elections in three distinct regions of the country:

Northeast. Primaries in Massachusetts and Rhode Island.

South. Primaries in Florida, Georgia, and Alabama.

West. Caucuses in Oklahoma, Washington, Hawaii, and Nevada.

There are also some less-important votes: a mail-in primary among Democrats abroad and a caucus in American Samoa.

Hart wants to show that he can win or at least run a strong second in every region of the country. That means doing well in Massachusetts, winning something out West, and certainly doing better than expected somewhere in the South.

Mondale's best hope for shutting out Hart could be the South. Hart ignored the region for months, partly for monetary reasons, partly for strategic reasons.

Hart's campaign manager says that earlier, the South looked like difficult territory for the senator. There were two regional candidates (Askew and Hollings). Jesse Jackson was expected to get the black vote. John Glenn was making the South the cornerstone of his campaign. Mondale was going full blast there in an effort to stop Glenn.

''It didn't seem to us that there was very much room for a Gary Hart, a little known senator from Colorado,'' says Mr. Henkel. But that's changed, and Hart is gearing up for a full-fledged battle in Dixie.