They seemed, at first blush, an unlikely pair to be heading a Washington lobbying group.

First, there was Jack Anderson -- the Pulitzer prize-winning newspaper columnist whose expose's once struck fear and loathing in the hearts of high government officials.

And then there was J. Peter Grace -- the president of the W. R. Grace & Co., whose zealous crusade against wasteful federal spending has made him one of President Reagan's best friends in the business community.

But the organization that Anderson and Grace formed a few months ago -- called Citizens Against Waste -- seems to have gotten off to a lightening start in its self-proclaimed blitzkrieg on government waste. The group, which critics describe as a sort of Common Cause for corporate America, already has raised more than $650,000 in individual and business contributions. Now it is about to launch a sophisticated public relations campaign that will use everything from budget deficit life preservers to the Green Bay Packers football team.

J. P. Bolduc, the group's hard-charging president, says that by selling $10 memberships to millions of irate taxpayers, Citizens Against Waste expects eventually to raise $10 million. That is more than enough money to finance a massive grass-roots lobbying campaign that will overwhelm the power of the "special interest" groups and pressure the new Congress into adopting the recommendations of the Grace Commission to cut the federal budget -- without any increase in taxes, he says.

"I'll get it, I'll get $10 million," boasts Bolduc, a W. R. Grace & Co. senior vice president who served as chief operating officer for the Grace Commission. "You have no idea of the kind of support we're getting. We're averaging 1,000 phone calls per day. We're getting thousands of letters a week. . . . The momentum is being created."

The early success of Citizens Against Waste is one sign of the increasing role that business lobbying groups are playing in the debate over the federal budget. Fearful that the deficit will intensify pressure for a business tax increase, business groups are trying to deflect the issue by mounting a preemptive strike for federal spending cuts, according to business lobbyists.

One new group, called the Deficit Reduction Coalition, which includes such mainstream organizations as the U.S. Chamber of Commerce, the American Business Conference and the National Association of Manufacturers, stoked the fires last week by calling for an across-the-board spending freeze that outdoes that proposed by the administration by including defense and Social Security.

"Business is running pretty scared," said Hank Cox, a Chamber of Commerce official. "They're determined to fight this budget reduction thing down to the wire. Because if you can't reduce the deficit by spending cuts, that leaves a tax increase -- and since the president has vowed not to raise personal income taxes, who do you think that leaves?"

The rallying cry for many in the business community is the Grace Commission -- the presidential panel of corporate executives, headed by Grace, that made 2,478 recommendations it claimed would save $424.4 billion over a three-year period. W. R. Grace & Co. is leading the charge with a new $2.6 million television and print advertising campaign that trumpets the commission's proposals.

But that effort will be more than complemented by a Citizens Against Waste advertising offensive that is among the more unusual in public policy debates. Big name and group endorsements have been solicited and everybody from Sen. William Proxmire (D-Wis.) to the Packers have signed on. Display counters have been designed that will be placed in thousands of supermarkets and convenience stores asking taxpayers to sign mass petitions demanding an end to the "squandering of government funds."

In addition, work is under way on Citizens Against Waste newspaper ads, billboards, bus displays, bumper stickers, T shirts, trash bags, life preservers, even a magazine that will include a centerfold with "the most absurd and obscene waste of the American Taxpayers' money that month."

"We're not an elitist group," explained Stan Cotton, a Florida business executive who is working on Citizens' media campaign. "Most of the public interest groups -- such as Common Cause or Nader -- they're best at giving expert testimony on the Hill, and they generally don't communicate to the lower people. . . . We know we have to look to certain symbols to explain our case."

While some independent authorities, such as the Congressional Budget Office and the General Accounting Office, have questioned the Grace Commission and concluded that many of its projected savings are exaggerated, Citizens Against Waste leaders are undeterred.

"What difference does it make how much you save?" asked Anderson in a telephone interview. "As long as it's waste, we're against it. . . . I'm sure that some of [the Grace Commission] task force reports are bad. I just haven't had the time to read them. They pile up five feet high. . . . But what I have had the time to investigate, I've found to be essentially good."

Anderson's belief in the issue runs so strong that he says he has even discussed it in private meetings with President Reagan and has won an endorsement of sorts for his efforts.

"I visit with the president occasionally and . . . yeah, I would say he's supportive of what we're doing," Anderson said. "But he tends to be supportive of everything you talk to him about."

How did Anderson and Grace get together in the first place? Anderson says it was his idea: A few months ago, he says he decided to revive an old tradition of his late partner, Drew Pearson, to become actively involved in a an issue of public importance.

"I've been negligent," he said. "I believe columnists should be crusaders for the public good. . . . Drew Pearson always had a project, he always felt the column should champion something. I decided it should be waste in government. . . which is the most pressing issue we have right now."

Although Anderson never met Grace, he says he was the natural person to contact in view of his work on the Grace Commission. Grace and his associate Bolduc jumped at the chance to work with the columnist -- in large part because of his image as "a journalist with liberal tendencies."

"We were accused of being partisan, Republican and pro-big-business, even though Peter has been a lifelong Democrat," said Bolduc. "So whenever you've got a perception that is wrong, you've got to change it."

The alliance caused some grumbling among Anderson's team of investigative reporters, partly because Grace himself is a figure of some public controversy. A recent study by Citizens for Tax Justice, a liberal group, showed that Grace's company paid no federal taxes in the past three years, while earning $684.1 million in profits. Grace was one of at least 250 big corporations that avoided taxes during that period as a result of the 1981 tax bill, according to the study.

To some skeptics, such as Fred Wertheimer of Common Cause, that makes Grace and his company a "special interest" that is no different than the special interests Citizens Against Waste says it is crusading against. But Bolduc, who is Grace's closest associate on these matters, says tax policy is completely separate from the issue of government waste. Anderson concurs.

"I don't agree with Grace on everything," says Anderson. "But on this one thing, we all agree. We're all against waste."