When Charles J. Walker heard a newscast announcing the passage of Proposition 13 in California last week, his eyes lit up and he let out a loud cheer. The 46-year-old Springfield, Mo., businessman had been harboring similar sentiments for a couple of years or more. What they did in California, he said, ecstatically, "was to show the state government they've had it. We need to do the same thing here."

Walker wasn't the only American taxpayer who cheered when he read about the California balloting. Throughout the country, taxpayers were openly gloating over the California effort's success. Pundits were hailing the measure as the start of a nationwide taxpayer's revolt. And conservatives were making plans for new efforts in other states.

The fact is, however, the taxpayers' revolt has been gathering momentum for quite some time, and the California balloting - spectacular as it was - was merely the latest manifestation. The revolution already has made itself apparent at the federal level in congressional reactions to spate of major tax proposals. And the property tax revolt has been simmering for years.

To many analysts, the protest represents a fundamental shift in the national outlook over the past several years - the end of the share-the-wealth philosophy of the late 1960s and its willingness to enact new social programs that redistribute income, cut taxes for the poor, and close tax "loopholes" that allow wealthy taxpayers to escape payment of taxes.

The new revolution is a revolt of middle-income and upper-middle-income taxpayers - for the moment, those in the $17,000 to $35,000-a-year brackets - who seem to be saying they think we have done enough - that income distribution has gone about as far as it should, that the tax system is as progressive as it ought to be, and that now it is time to provide relief to them as well.

Part of it obviously is the squeeze of inflation and rising tax burdens. The increase in prices has prompted wage boosts that push taxpayers into higher income brackets, leaving them with proportionally less take-home pay than they had at the end of the 1960s. And while Congress has cut taxes almost annually in recent years, most has gone to the lower income brackets.

But the revolt is more complex than simply a matter of taxes. Surveys by almost every major polling organization show it also is a protest against the performance of the government - frustration that the "bureaucracy" isn't delivering what it promised for the tax money. In effect, voters are deeply distrustful of government - and the tax issue is one way to slap back.

Burns Roper, whose Roper Organization has just completed a new in depth study of taxpayer attitudes across the nation, says voters aren't merely distrubed about high taxes, but about what they perceive as poor government performance as well. And Jay Schmiedeskamp, Gallup's chief consumer pollster, says the protest reflects a call for "a major reappraisal of priorities."

So it is that President Carter is having serious trouble getting a Democratic Congress to enact a sizeable across-the-board cut in federal income taxes this year, while at the same time the lawmakers are effectively tripping over themselves to pass such popgun tax measures as the tuition tax credit, and waffling over a rollback of Social Security taxes.

The new taxpayers revolt backfired on Carter. The Georgian correctly sensed taxpayers' frustrations in 1976 when he campaigned on a tax reform plan, but he misread what they wanted done about them. The "tax reform" the voters thought they were endorsing was tax relief, not more progressivity in the tax system. Carter's pledge to boost capital gains taxes really wasn't understood.

As a result, the president seemed mystified when his January tax-cut plan met such vigorous opposition, but the reaction was predictable: In traditional Democratic fashion. Carter proposed skewing his reductions below the crucial $20,000 to $30,000-a-year brackets. Many of his proposed "reforms" would hit taxpayers in these groups.

Rep. Abner Mikva (D-Ill.), a member of the House Ways and Means Communitee and an astute observer of taxpayer attitudes, says voters are suspicious of the traditional big Democratic tax cut plan, fearing ir won't really reach them personally, no matter what the politicians say. Indeed, Carter's proposal would result in a higher overall tax burden for four-person families making more than $23,000 a year.

What voters want instead, Mikva says, is something they can see plainly will provide tax relief for them specifically, without any mumbo-jumbo. Hence the support for the tuition tax credit and similar measures. The break may be less than a broad-scale tax cut would offer, but voters can see it and know it is there.

Some of the same sentiment has led to the collapse of the move toward "tax reform" - the long-held dream of liberals to close tax "loopholes" that primarily benefit high-income investors. In previous years, reform efforts were blocked largely by wealthy special interest groups. But today, Carter's package is being stymied by voter opposition.

Indeed, partly in response to this taxpayers' revolt, Congress now seems bent on undoing many of the key "reforms" enacted in the past decade. Thus there's broad support in both houses for a proposal by Rep. William Steiger (R-Wis.) to roll back the 1969 and 1976 increases in taxes on capital gains, and for a separate effort to repeal a 1976 increasing taxes on Americans living abroad.

And, as the Proposition 13 vote in California showed again, in many areas taxpayer frustration has mounted so that it is easy to muster support for drastic rollbacks in income or property taxes. So, in semirural Carrollton, Ga., GOP congressional candidate Newt Gingrich is finding surprising response to his support of a proposal by Rep. Jack Kemp (R-N.Y.) for an across-the-board cut in federal income taxes.

The revolt has many facets, but, in a word, the numbers simply haven't kept pace with the definition of middle class in this country. In the late 1960s, when many present taxing and federal aid programs were shaped, the middle-income brackets were $3,000 to $15,000 a year. The tax rates for those categories were relatively low, and many lower-middle-income families were eligible for aid.

But now, with prices and incomes rising - and both partners working in many families - middle-income often means a combined paycheck of $15,000 to $30,000 a year. Yet neither the tax rates nor the aid programs really have been adjusted fully. The result is, many of today's middle-income families feel they're in a bind.

The pinch stems from several factors: Inflation, of course, has cut into real incomes in recent years, undoing the huge gains that accrued in the late 1960s. And rising wages have pushed many taxpayers into higher brackets than they were before - subjecting them to taxation at higher rates. Social Security payroll taxes have risen sharply.And in many states, property taxes have soared in recent years.

Lawmakers have acted to provide some tax relief, but middle-income tax-payers recently have been short-changed because much of the big federal income-tax cut in recent years has been skewed primarily toward the bottom brackets. State and local property tax relief most often has been aimed at elderly homeowners. And existing tax "loopholes" help high-income groups most.

At the same time, there has been less opportunity for middle-income families to hedge against inflation by investing their money. Interest earned on savings accounts no longer keeps pace with inflation. The stock market has been in the doldrums for years. House prices have soared, but the profit for sellers often is so huge that much of it is eaten away by taxes.

Finally, the situation has been exacerbated by the tendency of Congress to aim most federal aid programs at the lower-income brackets - and out-growth of the 1960s. The result has left middle-income families with the brunt of the tax burden and the least opportunity for relief. Small wonder the taxpayers' revolt is at hand.

The problem shows up most clearly, perhaps, in the battle over the tuition tax credit. On its face, the measure is somewhat short of ridiculous. It would swell thje budget deficit by between $1.5 billion and $5.2 billion of existing revenues to give taxpayers a cut of between $50 and $500 a year.And in many cases, it would aid families earning $30,000 to $40,000.

But if the logic is difficult to understand, the sentiment behind the bill is not. For years, sending kids to college had been one of the middle class' accepted perquisites. While tuition was not proportionally much higher than it is today, a family could invest in stocks or an annuity fund to finance it. Or, in many cases, students could work their way through school.

But today, the yield from stocks or investment funds is proving hopelessly inadequate, and the jobs typically available to students pay only a minuscule share of a year's tuition cost. To top it off, many families now have two or three youngsters in college - a rarity in earlier years. And scholarship aid often is not available for those in today's middle-income brackets.

What's likely to emerge from the newly discovered taxpayers' revolt is difficult to predict - at least in magnitude, if not in direction. On the national level, the House Ways and Means Committee showed again last week it still is not sure which way to go on the president's package. There still is a chance it will scuttle the entire Carter bill.

And at the state and local level, while many states may consider tax and spending limitations, it is far from clear how effective they will be.

As it stands now, most experts expect the bulk of any new measures to be modeled after the one in Tennessee, which limits the growth in state spending to a proporation of personal income - not a very restrictive measure. Indeed, some analysts predict if the California action last week forces a major cutback in services, it may scare others away from any drastic moves.

Just the same, there is no getting around it: Middle-income taxpayers finally are beginning to make themselves heard. The taxpayer's revolt may not be new, but it is starting to take shape in a way that lawmakers can sense and react to. And that may be a significant development all by itself.