As he launches his fall campaign Monday with a coast-to-coast blitz, Democratic presidential nominee Walter F. Mondale is on his own.

His campaign organization has assembled a cadre of surrogates to rally the constituencies he will need behind him in the battle against President Reagan. His vice-presidential running mate, Geraldine A. Ferraro, has added a spark to the ticket. Poll data also show that on a variety of issues, Mondale's position is closer to the public's view than is Reagan's.

But it is up to Mondale to power this Democratic engine for the next nine weeks, party strategists and his advisers say. Mondale alone must answer the overriding question that stands between him and victory: Can he lead?

"Nobody can do that but Walter Mondale," said Raymond Strother, who was media adviser to Sen. Gary Hart (D-Colo.) during the primaries. "He's got to prove who he is, and his organization has to devote itself to damage control to make sure things don't get in the way. Now he stands alone."

There is nothing cosmetic about this challenge -- no "tinsel and hair spray," as Mondale has said. If the Democratic nominee is to let his hair down, as some have advised, it will remain properly parted on the left.

"He's not going to change his spots," one aide said. "So you've got a guy who's got to present his spots."

In his struggle for the nomination, Mondale liked to say that "What you see is what you get." As he left Minnesota this afternoon for New York, where he will begin the fall campaign with Ferraro, the watchwords seemed to be "Mondale, be Mondale."

His advisers agree that if Mondale is to become president, he has but 65 days to spell out his vision of the future for all Americans, not just for Democrats. He must be, they say, the "Fighting Fritz" of the primaries and take the fight to Reagan relentlessly, not haltingly as he has so far.

He must affirm that he is not the big-spending, ultra-liberal, un-American weakling with the hypenated name -- "Walter Carter-Mondale," as one Democrat put it -- that the Republicans have tried to make him.

Mondale already has lost precious time to party infighting, fence-mending and controversy, and he is well behind Reagan on the vital issue of leadership.

In a May poll by The Washington Post and ABC News, 73 percent of the registered voters interviewed said Reagan had strong leadership qualities, compared to 50 percent who considered Mondale a strong leader. The two ran about even when respondents were asked if each man could be trusted in a crisis.

In July, a similar poll found negligible changes on the perceptions of strong leadership, and 52 percent said Reagan was best for America's prosperity compared to 40 percent for Mondale.

Mondale had a 5 to 4 advantage when the questions turned to keeping the nation out of war and administering government programs fairly.

He also maintained a lopsided advantage over Reagan as a candidate identified with citizens' concerns rather than those of special interests, despite frequent allegations to the contrary.

One reason Reagan often is given an edge on leadership issues is because Mondale is chided for not having a comprehensive creed for America. But Mondale's aides say he has one, and they consider it just as red-white-and-blue as Reagan's.

"I stand for an America where we work together as being a part of the same family . . . . " he told an audience in Madison, Ala., recently. ". . . I want America to feel proud of itself for the right reasons . . . .

"I want you to hear me talking about human rights and democracy and justice, so that your values are reflected. I want you to see an intelligent president operating in foreign policy because he knows other societies . . . .

"I want to tap . . . in our people, a sense that there are no free meals, life is not easy, you gotta work hard . . . .

"But there's a joy in accomplishment, a joy in us pulling together and achieving . . . and dominating the world not because we're bragging and pushing people around, but because as Americans, we're so good that no one can catch up with us."

Those views are the wellsprings of the "new realism" Mondale outlined in his acceptance speech to the Democratic National Convention.

In that speech, Democrats say, Mondale showed he could not be "paled" in the presence of such powerful party orators as Jesse L. Jackson, New York Gov. Mario M. Cuomo and Sen. Edward M. Kennedy (D-Mass.).

Some said they considered his speech more effective than the one Reagan gave a month later, and cited it as evidence that Mondale could prevail over the vaunted "great communicator" in one-on-one confrontations.

That is one reason Mondale and his aides are pressing for nationally televised presidential debates.

The Mondale camp also is counting on Reagan to stumble, as he did on the tax-rise issue, and be forced away from a Rose Garden strategy that Mondale campaign manager Robert G. Beckel has equated with a "65-day photo opportunity."

James A. Johnson, Mondale's campaign director, said that Mondale will focus on several issues to enhance his leadership case. These include his willingness to "level with people" as he did by acknowledging that he would raise taxes if elected, along with the idea that he has a better plan for the future than Reagan does and would be more innovative in office.

This approach worries other Democrats. "I'm sure he's telling all the right things," said one strategist who has followed the campaign. "But they don't communicate it the right way. They don't understand what people want to hear, and they don't understand how much it takes to get into their psyches. They're searching. They're flailing."

Mondale, however, insists that he will continue to do things his way.

"I'm not going to reprogram myself. I just can't do it. I won't do it," he told a television interviewer in July.

"I have never lost an election when my name is at the top of the ticket. I have just won this nomination, the toughest in history," Mondale added. "Mr. Reagan's in for a big surprise."