In January 1966, Lyndon Johnson was a worried man. Not only did he have to cope with a fast-escalating war in Southeast Asia, but a new problem - inflation - was heating up at home.

Consumer prices the year before had risen 1.9 percent - up sharply from the 1.2 percent recorded in 1964. Home mortgage interest rates had climbed to 5.8 percent.

"Perhaps our most serious economic challenge in 1966 will be to preserve the essential stability of costs and prices," Johnson warned solemnly in his economic report to Congress. The following year, he would propose a surtax to flight inflation.

Today, 12 years later, Jimmy Carter would be grateful to have an inflation rate anywhere near Lyndon Johnson's 1.9 percent - an accomplishment that would make him an economic hero and most likely unbeutable in the next election.

The inflation rate for the first three months of 1978 has climbed to a decidedly uncomfortable 7.4 percent annual pace - already well beyond the 6 percent to 6.5 percent the White House projected in January would prevail for the year as a whole.

Yesterday Carter laid out his plan for dealing with inflation.It consists to a large extent of exhortation. He renounced wage-price controls, and said the government instead would lead by example, limiting budget outlays and this year's federal pay raise.

In part his speech was a confession of powerlessness. There are, Carter reminded his listeners and the voters, limits to what a president can do to retard wage and price increases in a private economy the size of this one. Inflation will come down only slowly.

The administration's Council on Wage and Price Stability fretted publicly this week that the nation may be "hopelessly stuck" with a rate of 6 to 6.5 percent. And many economists are predicting inflation will speed up even more later this year.

Mortgage interest rates, which created a national furor when they edged up to 5.8 percent in 1965, now are 8.9 percent and rising. New cars cost half again as much as they did in 1965, and supermarket prices - particularly in major cities - are double what they were then. Meanwhile, the purchasing power of American workers has barely held firm.

The story isn't a new one. Since Johnson's travail in the mid-1960s, inflation has been the bane of American presidents - and none of them has been able to conquer, or even faze, it.

Johnson's eventual acquiescence (in October 1967) to an anti-inflation surtax came too late to head off the impact of deficit financing of the Vietnam war in an already overheated economy.

Richard M. Nixon resorted to the nation's first preacetime wage and price controls - but prices made up the lost ground almost as soon as the government restraints were lifted.

Gerald R. Ford tried everything from budget-cutting proposals to "WIN" (Whip Inflation Now) buttons - but still wasn't able to bring inflation down to its pre-1965 levels.

Even that old economic castor oil - high unemployment - hasn't helped. Inflation slowed substantially after the 1974-75 recession, which was the longest and deepest in 35 years. But the jobless rate still is high, and inflation is picking up again.

Americans are becoming conditioned to high inflation, and are learning how to live with it - by linking wages and benefits to living costs. That process, known to economists as "indexing," helps blunt inflation's impact. But analysts warn it also helps create more inflation.

Union wage settlements, once involving long-term contracts and based almost solely on what was won at the bargaining table, now are shorter-lived and contain provisions for automatic cost-of-living increases. The more prices climb every year, the more wages increase - pushing up labor costs and prices.

Major government programs, such as Social Security benefits, are indexed to rise with wages and prices. And some economists even have suggested automatically adjusting federal income taxes each year to keep tax-payers from being pushed into higher brackets.

The inflation problem of recent years began with the start of the Vietnam war. The escalation in fighting and costs came just at the time Johnson was launching his Great Society spending programs. But he didn't want to raise taxes to pay for both efforts. So the economy overheated, and inflation gathered momentum quickly.

Nixon tried to slow the wage-price spiral by conventional means in 1969 and 1970, but the nation was in the grip of inflationary psychology. Finally, in a desperation attempt - and with a far-lower inflation rate than now - the Republican president turned to wage-price controls. For a while, they seemed to work.

But the illusion was shattered in early 1973 when increased worldwide demand bought about shortages in farm products in many basic raw materials - creating a new flare-up of inflation that more than offset whatever "good" the controls had done.

In October 1973 came the Arab oil embargo and accompanying increases in petroleum prices that rocked the world economy and sent inflation soaring again. On top of that, bad harvests pushed farm prices up sharply.

The nation headed into its first bout of "Double-digit" inflation in 25 years.

Since then, Americans have been involved in a game of catch-up that has kept wages rising sharply - pushing prices up continually. City workers have been catching up with farmers, union workers have been catching up with autoworkers. Now, all of them are catching up all over again.

Businesses have been trying to overcome rising labor costs. Others have been trying to keep up with rising materials costs. And now, as the economy enters its fourth year of recovery, many sectors of the economy are straining to stay apace of rising demand.

Moreover, government leaders have seemed almost powerless to do anything to stop the spiral. Nixon and Ford inveighed heavily against overspending, vetoing many spending bills, but Congress often overrode them. Carter tried to coax business and labor into slowing their demands, but was hooted down from the beginning.