"When I was in the Navy," Prime Minister James Callaghan began with a sly smile, "whenever we landed at Alexandria they would show us the three-card trick. It was a simple game really, after the cards were moved around, we were supposed to find the lady. But we never, ever found the lady."

It was Callaghan's way of explaining to reporters today the frustration he and his Labor Party felt campaigning against the opposition Conservatives and their leader, Margaret Thatcher, for the May 3 national election.

Callaghan has been trying to needle Thatcher and the conservatives into an angry battle that would wake up Labor's working-class supporters and frighten middle-class swing voters into keeping Callaghan as prime minister rather than gambling on Thatcher.

But Thatcher, whose Conservatives still hold a comfortable 10 percent least in most public opinion polls, has stayed cool in her bid to become the first woman prime minister in Europe.

With less than three weeks left until election day, she barely has bothered to campaign.

While Callaghan presented his party's election program a week ago, Thatcher waited until Wednesday, drawing an overflow crowd of curious reporters to Conservative campaign headquarters.

While Callaghan spent the past week in perpetual motion, holding daily press conferences and barn-storming the country, Thatcher seldom stayed far from her Chelsea home or her Finchley parliamentary district in northern London.

While Callaghan tried to distract voters from the sudden arrival of warm spring sunshine here this weekend, Thatcher joined most other Britons in taking a long-four-day Easter holiday.

Rather than campaigning primarily on his government's record in office or his party platform, Callaghan, although he is the incumbent, has been running against the Conservatives. Calling this a "watershed election" that amounts to a "campaign for the future of the nation," Callaghan has tried stern warning and biting sarcasm to convince voters that Thatcher and the Conservatives could be dangerous for the country.

He and members of his Cabinet have argued that the Conservatives' promise to make big cuts in both taxes and public spending will threaten more than a million government-subsidized jobs and the welfare state services enjoyed by all voters.

They also predict confrontations from the Conservatives' determiniation to curb labor union power as well as spiraling inflation from their promised shift from income taxes to consumption taxes for new government revenue.

"Public expenditure, yes," Callaghan told a cheering audience of Labor supporters in Glasgow last week. "Leths defend it, let's be proud of it. I have no hesitation in takin on the Conservatives on this issue.

"There is not a single part of the country that would not suffer from the Conservative policy of cutting the jobs program. They would turn Scotland, Wales, Northern Ireland and many regions of England into deserts of unemployment."

It would be, he thundered, "national suicide."

Rather than answering Callaghan and slugging it out toe-to-toe with him, as Labor had hoped, Thatcher has thus far projected the image of statesman-in-waiting, ignoring Callaghan's jabs to concentrate instead on patient explanations of the Conservatives' detailed blue print for change in Britain.

Anyone looking for the fiery Thatcher, who sometimes shot too quickly from the hip in the past, was bound to the disappointed by her low-key news conference presentation of her party's program. It pledges that the Conservatives will cut taxes, reduce government spending except for health, defense and criminal justice; sell nationalized industries like aero-space and shipbuilding back to private investors; take the government out of private industry wage bargaining; tighten immigration laws to reduce the number of new black and Asian immigrants from the Commonwealth, and hold a vote in Parliament for the restoration of the death penalty.

"What Britain needs," Thatcher said is measured tones, "is a steady change in the long term."

Although still appearing to be much less relaxed than Callaghan in this kind of public give and take, she scored several points in verbal sparing with reporters, an important ability in the school debating-team style of British politics.

She insisted that the Conservative manifesto, or platform, spoke for itself-and she quoted it verbatim-in tricky areas of foreign policy such as the question of recognizing the new multracial government of Rhodesia. In explaining why she wanted to cut taxes to give families more discretion in how their earnings were spent, she remined one senior British political writer that "choice is the essence of ethics."

Thatcher has left counterattacking Callaghan to her "shadow Cabinet" of parliamentary experts, who argued that the Labor government has been wasting taxpayers' money on a bloated bureaucracy and unwise public spending projects. The strongest attacks have come from a surprising source, Conservative former prime minister Edward Heath, whom Thatcher replaced in a tough Conservative Party fight after Heath lost two elections in a row in 1974.

There had been concern that Heath's personal animosity toward Thatcher and his deep disagreement with her on several fundamental issues would make him a reluctant campaigner. He has launched a vigorous national speaking tour, however, enthusiastically belittling Labor's record in government and urging that the Conservatives be returned to power, although he never mentions Thatcher by name. Heath also has been dropping hints that he would like a place in a Thatcher Cabinet.

As in the United States, the media play a central role in campaigns here. Although Thatcher refused to debate Callaghan, each will appear separately, as Liberal Party leader David Steel did this week, on a two-hour BBC television call-in show, and their aides debate each other on BBC radio call-in programs every day.

Most of the national newspapers here, particularly the tabloids, clearly favor one party or the other, in both their news stories and editorial pages.

The conservative-leaning Sun, which ahs the largest daily circulation, headlined its front-page coverage of Thatcher's campaign-opening press conference, "I BELIEVE!" and began its news story in bold type: "Tory leader Margaret Thatcher yesterday declared her faith in a better, brighter, booming Britain."

The Daily Mirror, which supports Labor and had given front-page coverage to Laborhs manifesto, made no mention on its front page of the Conservative manifesto or Thatcher's press conference.

It was one of Britain's serious newspapers, The Guardian, which supports Callaghan, that made the first allusion to the hidden issue of the campaign: Thatcher's sex and the fact that she once admitted publicly to sometimes being reduced to tears in the privacy of her home.

Her press conference Wednesday was a very hot affair in a stuffy, overcrowded room, and a front-page picture in the next day's Guardian showed Thatcher using a handkerchief to cope with the perspiration caused by the hot television lights, as did many of the men crowded into the room. But The Guardian's picture caption said she was using the handkerchief "to dab away the emotion." CAPTION: Picture 1, Prime Minister James Callaghan greets supporters while campaigning in Glasgow. UPI; Picture 2, Opposition leader Margaret Thatcher talks to a voter in her north London district. UPI