Long Beach, Calif. — Walter Mondale now begins the most crucial part of his fall campaign - building his case against the Reagan White House. Mr. Mondale, a poor second in the polls, has touched on four basic arguments this week that he hopes will finally begin to erode Mr. Reagan's support. The President is ahead in all but two or three of the 50 states.
Aides say the themes outlined this week will form the foundation of Mondale's entire fall campaign against Mr. Reagan. Some of the themes are familiar, such as the danger of budget deficits. One of them, an attack on what Mondale charges is an attempt by the White House to mix politics and religion, is risky. But a number of experts say Mondale must toss aside caution if he wants to have any chance of victory.
With the economy humming and the nation at peace, Mondale's task is clearly uphill. But the former vice-president says there are dangers and issues that will turn voters his way. These include:
The nuclear arms race. Mondale's first words as he opened his campaign in Merrill, Wis., on Labor Day were a challenge to Reagan on arms control. Reagan is ''the first President of either party since the bomb went off never to have negotiated any arms control,'' he charged.
Budget deficits. Mondale called the federal deficits a short-term threat to jobs and a long-term threat to the next generation. ''These deficits have killed 3 million of our best jobs,'' he says. ''Right now there is an obscene trillion-dollar debt building up on our children's shoulders.''
Fairness. Over and over again, Mondale calls on voters to help him make the United States a better place for all citizens, including the needy and the average working man and woman. His speeches are full of populist applause lines (''I refuse to make your families pay more so that millionaires can pay less''). He paints Reagan as a person of ''uncaring, icy indifference'' toward maintaining such programs as social security, medicare, student loans, and food programs.
Religion in government. Mondale aides think they have spotted a chink in Reagan's armor in the President's courtship of New Right fundamentalists such as the Rev. Jerry Falwell. Says Mondale: ''Those who seek to intrude government and the politicians into religion lack confidence in the wisdom and the decency and good sense of the American people. ... They doubt the steadiness of our faith.''
Throughout his attacks on Reagan, Mondale weaves his own vision of the future. Democrats are sensitive to the charge that they are naysayers - filled with gloom about America and critical of everything, and presenting the country with little that is new. Mondale praises Americans as ''a strong people.'' His picture of the future sees Americans using their strength for arms control, not arms buildups; for the Peace Corps, not for selling guns abroad; for making the country competitive again, not for running up federal debts that undermine industries, families, and farms.
Much of this has strong appeal, especially to traditional, liberal Democratic voters in the Northeast and Midwest.
Mondale's challenge at this point is to broaden his support, especially among four major groups: white Southerners, Westerners, Roman Catholic ethnic groups, and young, white professionals.
President Reagan has already gone a long way toward reaching out to all these groups. His support for a strong defense appeals to Southerners and ethnic groups, especially those ethnic groups with roots in Soviet-dominated Eastern Europe. The improved US economy, reduced inflation, and lower taxes all sit well with upper-middle-income Yuppies. And Reagan's attempts to remove restraints on free enterprise appeal to the independent spirit of the West.
Mondale's themes do little to reach out to these voters. He talks more about military waste than military strength. He talks of higher taxes more than reduced federal spending. He doesn't mention inflation. He vows to boost levies on business.
Mondale has, in recent speeches, steered clear of the so-called ''sleaze'' issue, which was once expected to be at the top of his agenda. The omission was probably out of concern that any mention of conflict-of-interest charges against Reagan appointees could revive the issue of the finances of Mondale's own running-mate, Geraldine A. Ferraro.
Mondale and his speech writers have clearly been doing their work. He and Ms. Ferraro peppered their speeches with Harry Truman-style lines that had their audiences shouting their approval.
''Working people are being pounded,'' Mondale told one audience. ''The big boys have been picking your pockets to line their pockets.
''To the 90,000 corporations who paid no taxes at all, my message is: Your free ride is over,'' he warned.
''To the defense contractors who charge $50 for a 50-cent light bulb, my message is this: The ripoffs are over.''
Ms. Ferraro also has some crowd-rousing lines. ''I want our government to give full support to our schools, not to lobby for tax breaks for segregated academies,'' she told crowds in Wisconsin and California. ''I want a government that takes polluters to court, and not to lunch.''
Comparing the two presidential candidates, she said: ''While Ronald Reagan was making movies, Fritz Mondale was making history as a champion of civil rights and social justice.''
This week's prelude that briefly touches all the Mondale themes will be followed by fuller development as the campaign proceeds.
The Mondale team feels it has some issues going its way - a view supported by a Gallup poll released this week. It showed that on some subjects, especially the danger of war, the environment, the needy, helping minorities, and women's rights, Mondale is substantially stronger than Reagan.
What Mondale now must do is prove he can capitalize on these strengths - and add new ones.