Unless its new visibility slows it down, a campaign that many people dismissed as farfetched could, very soon, force Congress to consider a balanced-budget amendment to the Constitution, try to set ground rules for the first federal constitutional convention since 1787, or perhaps wrestle with both huge problems at once.

The small crusade with such great implications has been the political sleeper of the year, an anti-spending, anti-Congress drive that had been endorsed by 21 states before it came to general attention when California Gov. Jerry Brown embraced the cause last month.

Since then, four more states (Arkansas, North Carolina, South Dakota and Utah) have signed on. That makes 25. Advocates, such as Jason Boe, Oregon senate president and head of the National Conference of State Legislatures, expect to collect the required 34 by this summer -- though opponents claim some of the resolutions are invalid.

Where did this startling movement start? Proposed anti-deficit amendments have been kicking around for years. So have convention calls on other issues.

The idea of combining the two apparently came to several men in scattered states about four years ago. One of those, state representative David Halbrook of Belzoni, Miss., recalled recently that he "was sitting around with some friends in the back of a drygoods store -- no kidding -- and we got to talking about what could be done, what could be done to get some handle on the [federal] government."

Meanwhile, in Maryland, state senator James Clark (D-Howard) decided that a convention call might arouse his congressional delegation, which had ignored his first appeal for a no-deficit amendment.

After getting their measures through their own states in 1975, Clark and Halbrook got together and got organized. Halbrook lobbied across the South. Clark recruited the aid of the National Taxpayers Union (NTU), a small Washington-based group best known until recently for issuing frequent lists of lavish or silly-sounding federal grants.

While using NTU's mailing lists and ties with other anti-spending groups, they worked primarily through informal networks of state legislators. Recently Clark and James Davidson, NTU's founder, did recruit one paid coordinator: George Snyder, a former Maryland state senator now based in Florida.

"If this isn't grass-roots," said Halbrook, "I don't know what is."

Instead of seeking much publicity, the movement's sponsors nurtured their obscurity to keep opposition down. "We put out just enough statements so we couldn't be accused of hiding anything," Davidson said recently. They also encouraged impressions that their project was outlandish and their resolutions about as meaningful as endorsements of apple pie.

Still, hundreds of minor crusaders plod through the country all the time without winning even one state. This effort has caught on because its themes have at least superficial appeal. Rightly or wrongly, "balanced budget" is a catch-phrase for economic stability, strong dollars and governmental self-control -- just as "deficit spending" symbolizes recklessness, inflation and general civic decline.

Clark summed up this brand of economic fundamentalism recently by saying, "People may not understand all the theory, but they know instinctively what's wrong." And when "what's wrong" seems to include an irresponsible Congress and a runaway bureaucracy, using the Constitution as a checkrein is a saleable idea.

Thus, in Virginia, where most proposed constitutional amendments get stalled for years, the balanced-budget measure went through both houses without dissent in 1966. In Oregon last November, two state tax-curbing measures were rejected, but an advisory question on the amendment plan, put on the ballot by Jason Boe, got 82 percent of the vote.

As the plan became linked with other anti-spending, anti-Washington protests, it attracted more notice and much more fire. Last year in Colorado, for instance, the proposal was backed noisily by tax-protesting groups and a bloc of aggressive, arch-conservative Republicans. It passed, but only after a legislative brouhaha.

Clark and Davidson had hoped to proceed quietly until they had perhaps 30 states in tow. Brown's leaping-in obviously shattered that strategy and touched off political jockeying that they cannot hope to control.

The publicity has also brought a scrutiny that the movement is not ready for. Their proposals are still vague; they have not yet endorsed any specific amendment language or proposed convention rules. Thus they are ill prepared to explain, for instance, what kinds of "national emergencies" might justify a federal deficit, or how convention delegates should be picked. And they now find national figures whose aid they had hoped to seek, such as economist Milton Friedman, advancing competing plans.

Moreover, the state-initiative strategy has become a dicey approach. Clark, for one, says he does not want a convention or expect one to occur; his aim has been to force Congress to submit an amendment to the states. But if apprehensions about a possible convention cause the drive to stall, Congress could easily put the amendment question back on the shelf. On the other hand, if state legislatures are not deterred, stopping at 30 or 33 states -- while congressional deliberations amble on -- could become difficult.

Congress and the country are just starting to focus on all the problems involved. But the next important decisions may be made in the remaining state legislatures, mostly in the East and Midwest. The immediate question is how many of those legislators recognize that their votes really matter, and that the issue is no longer as easy as apple pie.