DEMOCRATS are seeing a lot of Joseph R. Biden Jr. these days. The senator from Delaware is all over the map, from Virginia to New Hampshire, sniffing the presidential air.

Biden is much in demand as a star speaker, one guaranteed to rouse Democrats from the melancholy torpor in which they have languished since November. Biden recently went to Richmond for a Jefferson-Jackson Day speech, one of five he is giving this month.

It wasn't a true test of his oratorical abilities or his capacity for stirring sparks in the burned-out and broken-hearted. Virginia Democrats, unlike others, are awash in euphoria, still savoring their triumph of last November when they elected a woman as attorney-general and a black as lieutenant-governor. As the newly inaugrated governor, Jerry Baliles, said, "We have discovered the joy to be found in politics when you pull together and reach for your dream."

The Democrats were delighted with the evening, which had already turned into the largest fundraiser in their history. They were delighted with their handsome speaker. Secretary of Commerce Richard J. Bagley had heard Biden before and said "he has a way of really reaching your heart when he talks."

The speakers who preceded Biden engaged in ritual joshing about his aspirations. The governor said archly, "We are Biden our time."

Biden laid it on thick in return. "No matter what I do, I truly believe that the Democratic Party is much better off if Chuck Robb the previous governor runs for president on the national ticket" -- a statement that deepened the happy delirium in the ballroom of the Richmond-Marriot.

"Chuck Robb has changed the face of Virginia," he went on. "He has begun to change the attitude of the Democratic national party. The message is loud and clear," he added, without actually saying what it was.

The rest of the generalities about the party were similarly coded.

"Who are we Democrats?" he asked. Then, in a dig at the so-called Atari Democrats -- presumably the Gephardts and the Harts -- he replied, "not a coalition of programmatic initiatives."

"We are about opportunity, passion, excitement and a sense of adventure -- and real heart." That seemed to be a bid for the lately liberated Kennedyites.

The party in the late 1970s, he said, had fallen victim to "paralyzing complacency -- we turned back and adored our accomplishments." It was a subtle reminder that he is not a doctrinaire liberal unwilling to admit party failures. Virginians probably know he opposed busing in the Senate.

Having instructed them in how they should feel -- although not what they should do -- about the party, Biden went on to suggest ways they might feel about him. He is 43, he told them, a baby-boomer, but one who refuses to believe that his contemporaries are so bogged down with mortgage payments and pediatricians' bills that they have forgotten their glorious history.

"Just because our heroes were murdered does not mean that the dream does not still live," he said.

Biden seems to be competing with Gary Hart, the current front-runner, for the yuppies who gave Hart his start. But while Hart is elaborately cool in his approach to his age group, Biden is hot. His appeal is unabashedly emotional.

When he finished in a pyrotechnic burst of quotations from the Kennedys and Martin Luther King Jr., one newly elected member of the House of Delegates pronounced it "the finest political speech I ever heard." But a young black woman said crisply that she found it "long on rhetoric, short on substance."

Young Larry Framme, the Virginia party's vice chairman for operations, saw "a tremendous amount of appeal for voters between 25 and 45. "He calls all those old feelings out, but he talks about the future. Cuomo is a traditional liberal, and I think his time has passed."

Biden, who almost jumped into the race in 1984 at the prodding of Svengali pollster Pat Caddell, is "much tempted" this time. His family has given him the green light for a trial run but not yet for the big one. Biden's timetable was upset by the sudden Kennedy withdrawal. He had expected to spend this year in "batting practice."

Biden, a senator since 1972, is a liberal with differences -- he votes against federal funding for abortion, for instance. He is not a Senate mandarin, not associated with any particular issue. He can be independent, having been the only member of the Senate Intelligence Committee to vote against aid to the Nicaraguan contras in 1982.

His colleagues think he is a nice man with good instincts, but unfocused. In Senate Judiciary Committee sessions, he asks such wordy, windy, discursive questions that he often uses up his alloted time, leaving none for a response.

His emergence as a fiery stump speaker pits him against the party's premier orator, Gov. Mario Cuomo of New York, whom Biden sees as his only rival for the nomination. "He's the 300-pound gorilla in this thing," he says.