A methodical man who does not like to waste time, Sen. Orrin G. Hatch (R-Utah) has developed a routine for the mid-mornings, mid-afternoons and late nights when there are no speeches to give and no hands to shake in his reelection campaign.

He sits in an office, puts on a telephone operator's headset and, cued by aides who have made the calls, talks to voters identified as undecided by a massive summer phone survey of this small, tidy state.

"I'm just calling to thank you for the opportunity to serve you," says Hatch, 48, who adds that he would like a chance to serve six more years.

Despite an energetic challenge by Ted Wilson, 43, the personable Democratic mayor of Salt Lake City, and despite anti-Hatch fund-raisers throughout the country hosted by the world's most famous Utahan, actor Robert Redford, Hatch's odd-hour telephone calls and his hold on Utah's conservative soul have kept him in front.

He has called at least 1,500 undecided voters, expects to reach 7,000 before Nov. 2 and reports that at least 80 percent are coming over to his side.

Wilson says polls indicate that Hatch is about 9 percentage points ahead. Vince Breglio, executive director of the National Republican Senatorial Committee, says the gap is 14 points. Whatever, Hatch is ahead and Wilson has taken what in Utah is a desperate step.

He has begun to criticize Ronald Reagan.

Vermont and then Arizona were once the nation's most Republican states, but Utah has shoved them aside. In 1980, Reagan won 73 percent of the vote here to 21 percent for Jimmy Carter.

The virtues of free enterprise, family life and personal morality that are at the center of Reagan's Republican doctrine mean as much to members of the Church of Jesus Christ of Latter-day Saints, who comprise more than 70 percent of Utah's 1.5 million citizens, as to anyone in America. Even with the economy in a slump, Reagan's approval rating here remains at about 70 percent.

Like Hatch, Wilson is a Mormon. He has a personal warmth that contrasts with the senator's sometimes cold, patrician style. But for a Democrat to win here, Wilson acknowledged, "you've got to be a pretty conservative Democrat."

During a recent debate at a junior high school in Bountiful, where even the boys' restrooms seemed as clean as the Wasatch Mountain air, Wilson launched his version of an all-out attack on Reagan:

"I, like you, would like to see the president's program succeed. He's a decent man doing his best. But the program is not working, ladies and gentleman, it's failing," Wilson said.

In national Democratic party circles, Hatch has been seen for some time as an irredeemable right-winger ripe for a fall.

In January, Hatch's campaign manager, Michael O. Leavitt, said the senator showed only a 7 percent lead in the polls. Labor union lobbyists in Washington began to raise money to depose the man who, as chairman of the Senate Labor Committee, was sworn to block their every move.

Some of the anti-Hatch enthusiasm got out of hand. Some posters here last springsaid: "Wanted, Sen. Orrin Hatch . . . Dead $250. Alive 25 cents. Bleedin' Bad $400."

But Democrats here thought they had a chance. With Wilson, and his successful seven-year record as mayor, they at least had a tested and attractive candidate.

At the Bountiful debate, the Wilson touch had an impact on Don and Elizabeth Stewart. The Stewarts have the look of modern day Utahans -- slim and attractive, just back from a marathon race the weekend before, looking too young to have a 16-year-old son and four other children.

But Don's computer sales, to quote Elizabeth, have been "nonexistent" recently, and she has been substitute teaching. By the end of the evening, Don pronounced Wilson "a lot more together than I realized."

Wilson was warmer than Hatch, said Don, who liked Wilson's economic program: political pressure to lower interest rates, fairer taxes for middle- and lower-income earners, industry stimulants and help for small business.

Redford, a personal friend of Wilson, has hosted fund-raisers in Washington, New York, Philadelphia, Chicago, Los Angeles and at his own Utah ski resort. To Wilson's surprise, his campaign revenues have moved past the $1 million mark.

"I think [Redford] has been very effective in raising money from the liberal activist elite," Hatch said. He smiled, apparently because none of it has seemed to dent his lead significantly.

In response to the Democratic effort, Republican fund-raising has pushed Hatch's campaign revenues to a state record of about $2.5 million.

Last week, acknowledging his need to catch up, Wilson played his trump, an anti-Hatch television commercial featuring popular Democratic Gov. Scott M. Matheson.

"His interests and Utah's interests are too often not the same," Matheson said of Hatch while praising the state's other conservative Republican senator, Edwin Jacob (Jake) Garn.

Leavitt, unimpressed, said the Democrats were damning Garn and praising Hatch just two years ago when Garn was up for reelection. The Hatch campaign responded with pro-Hatch commercials featuring Garn.

At the debate in Bountiful, Hatch and Wilson were outwardly friendly and often agreed on issues. Both lambasted federal subsidies for tobacco growers -- smoking is forbidden to Mormons.

They support federal help for Utah's mining industries and a balanced federal budget. Wilson, but not Hatch, supports an immediate nuclear weapons freeze. The two men split most sharply on the economy.

"The next person losing their job is going to be somebody closer and closer to you," Wilson said. "We are on the verge of a national tragedy."

Hatch replied: "I remember in my early life when my father lost his job, when he didn't know where his next job was coming from . . . but if we keep interest rates down, keep inflation down, then unemployment will go down, too."

Then it was back to the telephones for Hatch. His calls have spread so far that one day he reached a condominium in the Heber City ski resort apparently shared by more than one family. The family with an undecided voter previously surveyed evidently was not there when Hatch called because there was a long pause after he finished his opening spiel.

"Orrin," said the man at the other end of the line, "this is Ted Wilson."