IS THE NATION HEADED for recession in 1979, or will economic recovery be extended? And is President Carter's jawbone-led inflation fight strong enough, or must the federal budget also be cut back sharply? The nation's capital is in the midst of a serious policy debate that has strong advocates on either side of these issues.

One contention, offered by the increasingly influential Federal Reserve Board Chairman G. William Miller among others, argues that Carter's stimulus program ought to be cut back, because the pace of activity looks better than it did at the beginning of the year, while inflation is clearly a more serious threat.

The counter-argument is presented by President Carter himself. He worries that any shaving back of the stimulus program - especially by reducing the size of his $25 billion tax cut - will cost the nation in terms of economic, growth and jobs later on.

THERE ARE PERSUASIVE debating points to support either contention. But I venture the guess that this is an argument that Bill Miller, with the support of conservatives on Capitol Hill, is going to win.

When you stop to think of it, a smaller tax cut would be an extrordinary development in a congressional election year. When it first was proposed, the assumption in this town was that the Democrats - with Republican help - would run the tax-cut goodies to $30 billion or $35 billion.

The affable Miller, who has won friends quickly in Washington, winces when you ask him his reaction to the almost standard line in news accounts that his rhetoric sounds like his inflation-fighting predecessor, Arthur F. Burns.

"It's a compliment, of course, to be associated with a man like Burns," Miller told me the other day in his office. "But I'm behaving like myself in what I think is a responsible way to the problems I found here."

And the No. 1 problem Miller has fingered is inflation. "I want to smack down inflation," he says. "Employment is up and unemployment is down, and the way to get a further reduction in unemployment is to control inflation.

IT'S PROVED TO BE a powerful argument. The influential Al Ullman (D-Ore.), chairman of the House Ways and Means Committee, confides that he'd like to lop $10 billion off the Carter tax package. But he thinks that a $5 billion reduction is politically more saleable - and he has no doubt that the administration will eventually cave in.

I asked Miller for his reaction to Commerce Secretary Juanita Kreps' observation that the nation now faces a growth rate of possibly only 4 percent this year, compared with the earlier estimate of around 4.5 percent. "If anything," Kreps told me in a separate interview, "we need (the full) tax cut even more than when it was first proposed."

Polite as always, Miller said he gives great weight to Juanita Kreps' judgement. But he sticks firmly to the view that "in a fourth year of expansion, the large (federal) deficit has to be looked at in financial market terms, and in terms of the dollar."

Kreps is probably right about the lower growth possibility, Miller says. He is using the same number himself. "But if we don't get inflation under control, we'll be in trouble sooner or later. We may be better off to take slower growth now than later."

FAILING A DETERMINED anti-inflation effort outside the Fed, he says bluntly, he will have to move toward higher interest rates that will choke off business investments and housing starts.

Carter economists, including Economic Councill Chairman Charles L. Schultze and inflation watchdog Barry Bosworth, argue that Miller is fighting the wrong inflation war when he concludes that the big budget deficit is the major cause of inflation.

They point out, as well, that some of the recent euphoria about the economy is probably misplaced: a probable real growth rate of 6.5 to 7.0 percent in the April-June quater, cited by Miller, is merely the snapback after underpar, negative growth in the first quater due to cold weather and the coal strike.

But Miller and money policy hold the key. If Miller carries through a policy that tightens credit and boosts interest rates, a tax cut of any size would not have its intended expansionary effect.

Will there be a showdown? Miller doesn't tip his hand. But anxious Democrats on Capitol Hill, having accorded Miller a honeymoon phase until now, are expected to demand specifics on his monetary intentions, now until he has been so explicit on his fiscal policy views.