The cast of characters trying to attach a balanced budget amendment to the U.S. Constitution range from true believers who have been pushing the idea for a decade to business lobbyists who until last month wouldn't give it a second thought.

Theirs has been a marriage of convenience at a moment of opportunity, brokered by a politically savvy, one-time John Bircher who sharpened his tax-slashing instincts as a member of Gov. Ronald Reagan's California cabinet.

The amendment, which has quietly amassed 61 cosponsors in the Senate and 221 in the House, is considered likely to pass Congress in this summer of its 12-digit deficit discontent. And it is given a good chance of surviving the ratification gantlet of 38 states.

Polls show that Americans overwhelmingly approve the proposal. The interest groups opposing it, led by organized labor, have their work cut out.

The amendment is the product of a labored compromise between the different ideological cells of the tax revolution. One section would require Congress to adopt a balanced budget each fiscal year, and the other would limit the growth rate in government revenues to the growth rate of the private sector economy.

Who's behind all this?

At one end of the spectrum stands James Dale Davidson, 35, an Oxford University philosophy, economics and political studies major who has spent all his adult life as chairman of the National Taxpayers Union, the grass-roots tax lobby he founded in 1969.

Davidson, who looks as if he wandered off the pages of an Evelyn Waugh novel in his red suspenders, flowered ties and monogrammed shirts, describes himself as an analyst of "those conditions that are necessary for a free society to flourish." His studies have convinced him that all that stands between democracy and "the guys who come along on the back of a flatbed truck" is a balanced budget.

At the other end of the spectrum stands the U.S. Chamber of Commerce, the nation's largest business lobby and one of the most fervent defenders of the status quo.

Until last month the Chamber had dismissed the balanced budget amendment as too rigid, too gimmicky and unworthy of the Constitution. Then, in a reversal, its board overrode the recommendations of its Banking, Monetary and Finance Committee and voted to support it. The specter of $100 billion deficits proved to be a powerful persuader.

Davidson, who does not mince words, can take this new support or, better yet, leave it.

"Frankly these are the most feckless people you will ever find," he says of all the organized business lobbies in Washington. "They spend their time worrying about which of their turkey industries should get a bailout, and they never get around to taking on the structural problems. It may be bad business for me to say it, but they're more trouble than they're worth."

Between these two hostile camps stands Lewis K. Uhler, 48, a southern California lawyer/land developer who dallied in his youth with the John Birch Society before pursuing a more mainstream political career that eventually led him to head a Tax Reduction Task Force for Reagan, then governor of California.

Uhler eventually hooked up with Nobel laureate economist Milton Friedman of Chicago and in 1975 founded the National Tax Limitations Committee. It has a sophisticated direct mail operation to bring in 600,000 members who support its $3.5 million annual budget.

But the pragmatic Uhler has been only too happy to incorporate the notion of a balanced budget in the amendment both groups are supporting.

"From a marketing point of view, the words 'balanced budget' are pure magic," says Uhler. Polls have consistently shown that between 70 and 80 percent of the nation supports a constitutional amendment to balance the budget.

Uhler has a healthy dose of marketing savvy. For the lobbying to get the amendment past Congress, he has surrounded himself with the best that money can buy: polls by Robert Teeter, public relations by Robert Gray, direct mail by Richard Viguerie, political consulting by David Keene and lobbying by Charls E. Walker.

While the NTU and the NTLC are coordinating efforts as they work Congress, there remains an undercurrent of friction. Davidson freely admits he is still "sore" at the way the NTLC stayed on the sidelines while his group slogged from state to state for seven years trying to build support for a constitutional convention to adopt a balanced budget amendment.

Organized labor and senior citizens groups predictably joined the fray. But so did some other special interest groups who feared that the call for a convention was a smokescreen to open up the Constitution for other changes.

As the opposition mounted, the number of states that supported the convention call stalled at 31, three short of the magic number. However, the drive was anything but a failure. It achieved its secondary goal of forcing the hand of Congress.

Now that the action has shifted to Washington, Uhler's group has taken center stage. He has skillfully assembled a broad base of business support, including groups such as the National Federation of Independent Businesses and the National Association of Realtors that have been involved in the issue for some time, and a host of somewhat more skeptical newcomers.

At the Capitol Hill rally for the balanced budget yesterday, Reagan met with members of a new 50-state organization of business and other leaders, headed by PepsiCo Inc. chairman Donald Kendall, formed to lobby for the amendment.