Convinced that President Carter is becoming increasingly vulnerable, California Gov. Edmund G. (Jerry) Brown Jr. is running -- and running hard -- for president.

Within the governor's inner circle, the assumption is that the only remaining question about a formal Brown candidacy is the timing of an official announcement. In what Brown's aides call the "prepresidential" stage of the campaign, the governor's strategists are concentrating on paying off Brown's campaign debt from his 1978 reelection bid, raising funds for a prospective challenge to Carter in the 1980 primaries, and mapping the strategy for the major vehicle for a Brown campaign this year -- the national drive for a constitutional amendment requiring a balanced federal budget.

Brown himself has dropped almost all disguise about his ambitions and no longer muffles his criticisms of Carter. Campaigning hard in behalf of his proposal for an amendment for a balanced budget, Brown describes the administration's present deficit course as "nonsense and dangerous."

When a television reporter this week asked Brown whether rejection of his proposed amendment by the California Legislature would put "a crimp in his presidential plans," Brown answered in the negative.

"I don't think it will," he said. "I'll just take up the cause elsewhere."

Such open displays of presidential interest are becoming increasingly frequent for the 40-year-old governor, who defeated Carter in the primaries in states where the two candidates confronted each other in 1976.

Brown intimates emphasize that the governors' decision is not irrevocable. They point out, however, that Brown has to start now if he is to avoid the mistakes of 1976, when belated entry into the race gave him no realistic chance for nomination.

Early advertisement of his availability, say those close to Brown, will put him in a position to challenge Carter in the primaries if the administration is crippled by recession, runaway inflation, an energy shortage or any combination of the three.

"The go or no-go decision will be made much closer to the event and will be based at least in part on Carter's standing in the country," says one intimate. "But it's obvious that some territory has to be staked out before then to give Jerry the opportunity to run."

In a long and casual interview last week at his favorite Mexican restaurant, Brown said he will announce within a month the formation of a national campaign organization that will seek approval of his proposal for a constitutional amendment requiring a balanced federal budget.

The immediate goal of this organization, which probably will be headed by his longtime political associate, Tom Quinn, will be to convince Congress to originate the amendment. Failing that, Brown said, he will persist with his call for an unprecedented constitutional convention "with adequate safeguards" that would accomplish the same purpose.

The new organization, Brown said with a smile, will be "a nonpartisan and nonpolitical one that will meet all the guidelines of the Federal Election Commission." The presumption in California is that it will also become the nucleus of a future Brown-for-president campaign.

It is Brown's view that Washington institutions -- he specifically mentioned the White House and The Washington Post -- significantly under-estimate both the validity and the political appeal of a balanced federal budget.

"The people outside Washington see what is going on," Brown said, in comments similar to those once made by Jimmy Carter. "The people inside Washington aren't facing up to reality."

The swift pace of approval for the amendment through state legislatures offers some indication that Brown may be right at least about the political appeal of the idea.

Since Brown voiced support for the proposal in his second inaugural address Jan. 8, three additional states -- North Carolina, Arkansas and South Dakota -- have passed resolutions calling for enactment of the budget-balancing amendment. Twenty-five states have now passed such amendments, and Brown said he is willing to give assistance to pending proposals in at least three other states.

Under the Constitution, a convention must be held if 34 states petition for it. Brown, however, says he is convinced that Congress will originate the budget-balancing amendment if a convention appears likely.

The California governor derided a "chicken little" attitude of those who feel that a constitutional convention, which the American Bar Association has said could be limited to a single topic, could degenerate into a rewriting of the Bill of Rights. And he paints a near-apocalyptic vision of what will happen to the United States if it doesn't balance the federal budget.

Over rice, beans and white wine at the El Adobe restaurant here, Brown talked in detail about declining worker productivity, erosion of the dollar and increasing dependence on decisions of foreign bankers and oil producers.

Brown believes that the New Deal is dead. His answer to those critics who see a balanced budget triggering a recession is that a sever economic downturn and probably a depression is inevitable unless the United States puts its economic house in order by "strict self-discipline."

After winning reelection last November by a 1.7-million-vote margin, Brown has little doubt that he is the person best able to explain "the new realities of the 1980s" to the nation. And he is more open and direct than he used to be about the political consequences of his position. Where he once answered questions about his own future with a coyness bordering on irritability, Brown no longer shrinks from acknowledging that his position casts him as a likely presidential candidate.

"Obviously, there is a relationship between the quality of an idea and the opportunity to advance by it," Brown said last week.

For Brown, most of this opportunity appears to lie in his national advocacy of the balanced budget proposal and the hope this will catch on as Proposition 13 did in California. But he has discreetly sequestered a few eggs in other political baskets. In recent weeks, for instance, Brown has:

Named legislative liaison Tony Dougherty to head an organization, "Californians for Brown," whose mission is to pay off an $800,000 debt incurred in the reelection campaign. This is a prerequisite to any presidential fund-raising, especially since some of the money is owed persons who are considered prime 1980 donors.

Sought in a number of ways to allay the fears of labor leaders about his budget proposal. In a "state of the state" message far less publicized than his inaugural address, Brown pledged "to increase our benefits in workman's compensation and unemployment insurance and bring them into line with the inflationary reality of today." He also has wooed independent labor leaders, notably maverick George Hardy, head of the 650,000-member Service Employes Union.

Tried to keep restive liberal and minority leaders in line by a series of visible job appointments. Brown has appointed far more minority leaders and women to key state jobs than any of his predecessors.

Made it a point to take an early role in the campaign of Jewish groups to eliminate or extend the statute of limitations on Nazi war crimes, due to expire in West Germany at the end of 1979. Since his earliest days in politics, Brown has been highly sensitive to the issues favored by Jewish constituents. The only asset he owns other than real estate is a $10,000 Israel bond.

In advance of his national campaigning, and his coming battle with the legislature, Brown has shaken up his staff. He apparently intends to name Quinn to head the national campaign organization for the constitutional amendment.

Regardless of what Brown does organizationally, he appears to have clearly tied his political fate to the receptivity of voters to the budget-balancing issue. That is just fine with the governor, who believes he has grasped the issue of the future.

"America right now is not building for the future but stealing from it," Brown says. "I don't think that's what the American people want."