Yes, we need a significant cut in the American budget deficit. But when Wall Street and other fragile markets tell political leaders all over the world to ''Get to work!" the message has a broader and deeper meaning.

It would be a mistake to think that a nod in the direction of fiscal sanity will be enough to avoid the deep recession that analysts think likely next year. There remain the critical issues of the trade deficit, exchange rate levels, the protectionist threat and the ugly overhang of $1 billion in Third World debt.

At a dinner here Monday among liberal Democrats and members of the West German Social Democratic Party, Gina Despres, a top aide to Sen. Bill Bradley (D-N.J.), heard no disagreement when she said:

''The problems and the solutions we face are international: America can't solve this crisis alone. Just cutting the American budget deficit won't help unless West Germany and Japan expand their economies. It will only cause recession.

''If you {Germans} don't expand, we will have a bitter protectionist reaction, and we will all go to hell in a handbasket.''

Wolfgang Roth, a member of the German parliament and the SPD's ''shadow'' economics minister, acknowledged that confidence must be restored in the ability of the major governments to work together. Treasury Secretary James A. Baker III, Roth said, ''was right to criticize the Kohl government's high-interest-rate policy. It doesn't make any sense, and I couldn't justify it in any way.''

Yet the markets are just as unsure whether West Germany, which plays such a key role in Europe's economy, will face up to its responsibilities as they are about the U.S. government's ultimate response.

In Washington, politicians are still fingering each other for blame in the crisis. But what financial markets await is a fast and credible move (no smoke and mirrors, please) to cut the budget deficit significantly, not just the $23 billion that would arise anyway out of the Gramm-Rudman-Hollings legislation.

Financial markets need the assurance of a deficit reduction on the order of $40 billion to $50 billion in fiscal 1988. That would offset the inflationary potential of the Federal Reserve Board's welcome market-rescuing, money-easing steps that reversed its tight money policy.

In a telephone conversation Monday, New York Gov. Mario Cuomo said: ''If they {the White House and congressional budget negotiators} come back and say, 'We've giving it our best shot, and we can't come up with more than $23 billion,' then we've got to say: 'It's not enough, you've got to do better.' They need to send a signal that they are sensitive to this issue.''

One senses that President Reagan is not sufficiently scared. He temporizes about a tax increase, arguing that nothing worse than a ''correction'' is taking place, and that the economy is pretty much okay.

But how about the Democrats? I don't hear the half-dozen or so Democratic presidential candidates using the dreaded words ''tax increase.'' As political analyst Ted Van Dyk says: ''The Democratic presidential candidates' economic proposals have been, to this point, a joke.''

The idea of a tax increase must be put in perspective. Several readers, recalling that higher taxes in the 1930s exacerbated the economic decline then, wonder about the wisdom of raising taxes now. It's a good question. But no one is suggesting a Hoover-like tax program, designed to wipe out the deficit. Rather, it must be a carefully balanced package to reduce the deficit -- and be coordinated, as Gina Despres said, with offsetting stimulating moves by the Fed here and governments abroad.

Despite assurances by supply-siders that lower tax rates would generate larger revenues, the deficit was created by the huge 1981 tax cut. In turn, the deficit (financed largely by foreigners) set off high interest rates, an overvalued dollar and enormous trade and current account deficits.

With the fiscal policy so loose and stimulating a consumer boom, the Fed necessarily followed a tight monetary policy. That's why interest rates had been shooting up this year and became one of the elements underlying the stock market collapse. That's also why the budget deficit has to be curtailed -- so that interest rates can come down and stay down.

Then there is the question of the trade deficit and protectionism. One of the triggers for the Great Depression, most scholars now agree, was passage of the misguided Smoot-Hawley Tariff Act in 1930, after the market crashed in 1929. Yet you can search the Congressional Record fruitlessly for a statement by any protectionist that it would be better, now, to put aside any notions of trade restrictions.

Imagine the tonic if Democratic trade hawks, led by Rep. Richard Gephardt of Missouri, were to announce that they were abandoning their protectionist mischief that panicked financial markets.