He once walked on the moon, but here in New Mexico, Sen. Harrison H. Schmitt is just another earthling.

Wearing jeans, boots and a western shirt, and sporting a belt buckle bearing the name "Jack," he is standing in a small office across the street from the county courthouse on a windy afternoon, to greet voters at the town's annual Heritage Day festival that features everything from tacos to egg rolls.

But first come obligations to the media. A radio reporter walks up to the junior senator from New Mexico and introduces herself. "And I assume," she adds, "that you are Sen. Schmitt."

Greetings like that, and what they represent, have had Democrats drooling for more than a year over the prospect of winning back a Senate seat here in November.

Six years ago, former Apollo astronaut and native son Jack Schmitt drove the state in his red pickup truck and trounced the troubled Democratic incumbent, Sen. Joseph Montoya.

Since then he has performed studiously, if in relative obscurity, calling himself "an ideology of one" seeking solutions to the problems of the future and concentrating on issues of science and technology.

In Washington, he is overshadowed by fellow Republican Sen. Pete V. Domenici, chairman of the Senate Budget Committee and a politician of near-hero proportions back home. So when he shakes hands with voters these days, Schmitt doesn't take anything for granted.

"I'm Jack Schmitt," he says to a couple leaving the festival here. "Sen. Schmitt."

Schmitt, 47, is an ardent supporter of supply-side economics, to the point of criticizing President Reagan for backing the $98.3 billion tax bill approved by Congress in August. It was, says Schmitt, a sign of "unnecessary panic" by the president and Republican leaders in Congress.

Says his opponent, "Ronald Reagan has shown more concern for adjusting to reality than Schmitt has."

"You're not going to balance the budget by raising taxes," Schmitt says.

Even on this matter of principle, however, Schmitt's record is marred. He voted for the tax bill when it passed the Senate, reversing his position later when the bill returned from the House for a final test.

Schmitt's positions on other issues also have left him vulnerable. The League of Conservation Voters gave him a rating of five last year, the National Council of Senior Citizens a zero.

Why then is Jack Schmitt a clear leader in recent public opinion polls in New Mexico?

Meet Jeff Bingaman. The handsome attorney general and Democratic candidate for the Senate is standing in a crowded room in an Albuquerque hotel next to Massachusetts Sen. Edward M. Kennedy, who has come to campaign for the entire Democratic ticket. Now it is Bingaman's turn.

"Last night in Santa Fe, Sen. Kennedy said, 'What on earth has Harrison Schmitt ever done for New Mexico?' " he says, pausing for his punch line.

"I think that's a good, uh, point," says the candidate, also making the point that it isn't just everyone who can tell a joke.

Bingaman, 38, was a successful lawyer before he became attorney general four years ago, and he still sounds more like an attorney than a candidate.

As a result, his campaign has had trouble getting started.

A variety of polls have showed him 8 to 20 points behind Schmitt. The latest puts the margin at 14 points, with Bingaman gaining.

More troubling, however, is the fact that Bingaman has been running poorly in the heavily Hispanic areas of northern New Mexico, usually a Democratic stronghold. Other Democrats blame it on his reserved style and lawyerly manner.

"Jeff just lacks an instinct for the jugular," says a fellow Democrat.

Take Social Security. Three times, Schmitt voted against the minimum benefit, only to change his position when Reagan decided the Republicans shouldn't take the political heat on the issue and said he wanted it restored.

It took Bingaman until last week to challenge Schmitt on the subject in his advertising, and when Schmitt immediately hit back in radio ads charging Bingaman with "mudslinging," the mild-tempered Democrat was temporarily rattled.

"That bothers me," he says. "We have gone out of our way to state exactly what he did."

Even as Bingaman was calling a press conference to challenge Schmitt's claim that he turned around the president on the minimum benefit, he had difficulty working up any emotion on the subject.

"Sen. Schmitt has gone to great lengths to misrepresent his vote -- no, that's not fair," he says.

Bingaman also has been slow to decide how to handle Schmitt's plan for a mandatory, private retirement program for workers who turn 40.

"It's absurd," he said of the plan. "I haven't said much about that, but we're going to start talking more about it."

The lackluster campaign style on the part of these Harvard-educated candidates who grew up in the same small New Mexico town doesn't hide philosophical differences that give New Mexico voters a clear choice.

Schmitt says the economy is improving, that what the Reagan administration has done has not had much effect on the public, that the recession is the legacy of the Democrats and that further budget cuts along with continued tight money are needed to restore economic growth.

Bingaman disagrees and has picked five fights with Schmitt, on Social Security, the general direction of Reagan's economic policies, education funding, defense increases ("He's given the Pentagon a blank check," says Bingaman) and the environment, where Schmitt's support of the policies of Interior Secretary James G. Watt has drawn a rebuke from the Democrat. The political environment here led both parties to believe they could win.

Democratic in registration, conservative in attitude, the state has elected Democratic governors and senators but is represented in Washington now by two Republican senators and two GOP congressmen.

Schmitt now appears to have a comfortable lead, but with unemployment above 10 percent, the economy and the Social Security issue could make it closer.

Schmitt has worked diligently on his campaign organization, and if the feelings of the people at the Heritage Day festival are a guide, this election may turn less on public attitudes toward Reagan and various national issues than on money -- Schmitt will spend $1.5 million, about three times Bingaman's budget -- organization and incumbency.