Gov. Edmund G. (Jerry) Brown Jr. today challenged President Carter, Congress and the nation to heed the lesson of California's tax revolt and enact a U.S. constitutional amendment requiring a balanced federal budget.

Brown made the proposal in his second inaugural address, which he delivered over a statewide television and radio hookup rather than before the customary state legislative session. Brown urged California and other states to insist upon congressional approval of the amendment and demand a national convention to accomplish this goal if Congress refuses to act. He also supported a state constitutional amendment limiting state and local government spending.

"A constitutional convention to propose an amendment to balance the budget is unprecedented, but so is the political paralysis that prevents necessary action," Brown said.

Twenty-two states, acting under a federal constitutional provision which allows states to petition Congress for constitutional amendments, already have adopted proposals similar to the one advocated by Brown.

Tom Quinn, a top Brown political strategist, said the California governor hopes "to give leadership and focus to this movement." Congress must convene a convention if 34 states adopt formal resolutions requesting one.

Brown's speech signaled a secondterm national political strategy based on a fiscal conservatism surpassing President Carter's and, in some cases, that of his California precedessor, Ronald Reagan.

In phrases similar to those used by Reagan during his eight years as governor, Brown blamed government for fueling an inflation he said was "as destructive to our social well-being as an invading army."

But Brown's actual proposals went far beyond anti-inflation rhetoric. He called upon the California legislature to enact a new $1 billion tax cut which is likely to have widespread support among Republicans and vocal opposition from teachers, minority groups and segments of organized labor.

He proposed the reduction of 5,000 state government positions. And he said that everyone in government would have to become "more productive" in the years ahead.

The 40-year-old Brown, whom many in California believe will be a presidential candidate in 1980, said the nation should learn from Proposition 13, which has already cut California property tax revenues by $7 billion, that "the established political union and corporate powers are no match for an angry citizenry recoiling against an angry citizenry recoiling against an inflationary threat to their homes and their pocketbooks."

Brown left no doubt that he believes the federal government is now the primary "inflationary threat."

"People know that something is wrong when the federal government stimulates inflation and inflation raises the face value of prices, income and property so that taxes on each grow higher and higher," Brown said.

"This perverse government money machine has created a fiscal dividend for local, state and federal government and allowed all three to expand faster than inflation and faster than real economic growth," Brown continued. "These unauthorized dividends are now being canceled. The tax revolt is being heard."

Brown's carefully prepared speech, far more detailed than his first inaugural message, dispelled any lingering doubts that he has political ambitions extending beyond California's borders.

The inaugural address coincided with the creation of a new organization, Californians for Brown, which has as its immediate goal the repayment of $800,000 in loans made to Brown's successful reelection campaign. It is being headed by Anthony Dougherty, now the governor's legislative secretary.

"I don't know whether Jerry is going to run for president and I don't think he knows," Dougherty says. "But I wouldn't be taking this job if I thought it's only purpose would be to pay back campaign loans."

Brown's decision to seize upon the proposed federal constitutional amendment apparently was the product of a long and careful search to find an issue upon which he can nationally express his fiscal conservatism in a popular political manner.

As Quinn sees it, many of the resolutions calling for the balanced budget or the alternative constitutional convention are in conflict. He said that Brown hopes to find an acceptable formula that would address the issue coherently and that would strictly limit a constitutional convention to the single question of a balanced federal budget.

Brown's political course is likely to squeeze President Carter between Democrats of the left who want the party to reinforce New Deal-style social programs and fiscal conservatives who would like Carter to match his own rhetoric with actual balanced budgets.

This poses a difficult but not necessarily impossible challenge for Carter, observed former governor Edmund G. (Pat) Brown today in an interview in which he compared Carter's position with that of President Truman in 1948.

The senior Brown. still ebullient and politically interested at 73, said he doesn't think that Sen. Edward M. Kennedy (D-Mass.) will run against Carter and said he isn't sure that his son will seek the presidency either.

But Brown, while predicting that the political pendulum in California ultimately will shift back from conservatism to social concern, said that Jerry Brown's present positions are the ones in which he truly believes.

Brown observed that his son had spent three and a half years in a Jesuit seminary and said that "you can't take vows of poverty for that long a period of time without having them rub off on you." And he recalled an exchange in the recent gubernatorial campaign between his son and Republican challenger Evelle J. Younger.

During a televised debate, Younger said that Brown lacked "the Irish charm of his father," to which Brown replied that he possessed "the fiscal frugality of his mother."

"They were both right," the senior Brown said.