On a dreary, gray day in a town dominated by college students whose age group generally favors President Reagan, the Democratic challengers found the biggest crowd of their campaign and enough enthusiasm to help fuel their new-found momentum.
Three hours before the noon rally Friday, supporters began gathering on the lawn of the state capitol. It was ''the best-looking crowd I've seen all year,'' said an ebullient Walter Mondale, before the estimated 25,000 people.
Clearly, the vice-presidential debate of the night before had not dampened Democratic spirits, as Mr. Mondale and running mate Geraldine A. Ferraro made a joint appearance in Madison.
Mondale delivered some of the most effective lines of his campaign, arguing that he is the candidate of the future and accusing the Republican party of ''grave robbing'' when it evokes the memory of popular Democratic presidents.
Of President Reagan's trip aboard Harry S. Truman's famous whistle-stop train , Mondale said to loud cheers, ''Mr. Reagan, you may be on the right train, but you're on the wrong track.''
But the strategy for the Democratic challengers to get their own trailing campaign on track is not big rallies. It is debates. Both Mondale and Ferraro last week continually reminded voters of Mondale's strong showing in his first debate with Reagan.
''I beat George Bush, and George Bush beat Ronald Reagan,'' was the line Ms. Ferraro used at every stop, following her own debate. Mondale issued calls for an apology from Mr. Bush for accusing Ferraro of saying during the vice-presidential debate in Philadelphia that Americans had died ''in shame'' in Lebanon.
It was all part of an effort to keep the debates very much alive in the public mind, while the Republicans attempted to put even the vice-presidential debates aside.
''The fact is, the day after, we'll be pushed back to Page 16,'' said Peter Teeley, press secretary for Vice-President Bush on the morning after the Bush-Ferraro face-off. His prediction proved wrong. As Bush talked to longshoremen in New Jersey, he let slip a vulgarity in boasting of his debate performance, and the gaffe led many newspapers and television news shows.
Meanwhile, campaign workers in both camps held that the vice-presidential debate would not greatly affect the presidential race. ''I don't think the result of this particular debate is going to make a big difference,'' GOP pollster Robert Teeter said after the Bush-Ferraro meeting.
In a variety of surveys, listeners rated Bush's performance, which was more animated, higher than Ferraro's. Even among her fans at campaign stops in the Midwest, some gave Bush higher marks.
''I think, honestly, Bush won the debate,'' says James Perkins, an Evanston, Ill., lawyer who has supported Ferraro since before her nomination. ''I think Gerry was too subdued and looked down too much.''
But campaign workers, both publicly and privately, express little concern about that view. Their aim was to offer not the feisty, spontaneous quipster that she can be at political rallies, but a serious leader.
''We think her leadership numbers are going to go up,'' says Ferraro press spokesman Francis O'Brien, referring to opinion-poll results. Mr. O'Brien says the public ''did not tune in to see George Bush,'' because they know his credentials. The question was whether or not Ferraro was qualified.
As a result of the debate, ''she passed that threshold,'' the spokesman said.
''I think I projected what I wanted to project,'' the vice-presidential candidate told reporters later. She wanted to show she was ''capable of leading the country,'' and it was ''not a time to be flip.''
The performance seemed to have been tailored for voters like Karen Munger, a De Paul University law student who voted for Ronald Reagan in 1980. Before the debate, she says, ''I had never heard her speak,'' but had heard press reports of her ''raspy voice'' and ''nervous, unpolished'' speaking style.
Now that she has seen for herself, Ms. Munger was satisfied with Ferraro and has decided to vote Democratic.
There may be only a few such ''converts'' for the Mondale-Ferraro ticket as a result of the vice-presidential debate. The big accomplishment, according to the Ferraro spokesman, is that she will not be a ''drag'' on the ticket.
Although Republicans agree that vice-presidential events are not crucial for the race, they were clearly taken by surprise by Ferraro's understated debate performance. ''I expected more verve,'' says Vic Gold, a senior adviser to Bush. ''Everybody was saying, 'She'll kill him - that Ivy-Leaguer wimp.' ''
In fact, Bush was far more energetic in his responses, looking directly into the camera and often gesturing - perhaps too much, according to some observers. ''That's the way he talks,'' says Mr. Gold. ''He waves his hands.''
Reagan-Bush campaign director Ed Rollins told reporters Friday that he had doubts about Ferraro's qualifications. ''I just don't think that she shows the experience that the American public wants in their leadership,'' he said.
If that view is shared by many Americans, it was not apparent along the Ferraro campaign trail during the weekend, where she was back in full rally form , greeting thousands of supporters like those who filled the gymnasium to the rafters in the Chicago suburb of Hinsdale, a Republican stronghold.
The race is ''getting hot,'' and the incumbents are ''feeling the heat,'' she proclaimed at these events. If that is so, the heat is not yet turned up high, since the Mondale-Ferraro ticket is still trailing badly in virtually every state.
Representative Ferraro spent much of her post-debate time focusing on one relatively small state, Iowa, which is one of the few in which the Democrats are within striking distance of the President.