Following the agonizing controversy over deployment of Pershing II and cruise missiles in Europe, the NATO allies are facing another potential crisis, this time in their quest to cut dependence on nuclear weapons by improving their conventional defenses.

Politicians on both sides of the Atlantic say they want to respond to public anxiety about nuclear weapons by enhancing the North Atlantic Treaty Organization's ability to resist an attack by Warsaw Pact forces through conventional means alone. But the issues of how to pay for the extra military insurance and where to place the emphasis in an allied conventional buildup are causing conflict.

The Reagan administration is planning to spend as much as $100 billion during the next five years on fighter aircraft, more ammunition and better equipment for U.S. forces in Europe.

But U.S. strategists note that the enormous investment could prove futile unless the Europeans improve their basic defense infrastructure, such as runways, air hangars and bridges, to accommodate the bolstered American forces.

At the same time, pressure is growing in the U.S. Congress to insist that the European allies stockpile as much as 30 days' ammunition so their armies could fight for an extended phase at the start of any attack to allow more time for troop reinforcements to arrive from the United States.

Gen. Bernard Rogers, NATO's supreme commander, has said he would be compelled to ask for authority to use nuclear weapons "fairly quickly" in any Warsaw Pact assault, largely because of the dearth of NATO ammunition stocks.

When pressed by several NATO ambassadors last year, Rogers reportedly said that he would probably need to ask permission to "go nuclear" seven to 10 days from the outbreak of hostilities.

The estimate is based in part on the assumption that some West European countries would run out of ammunition within five days and be forced to surrender unless NATO escalated its response by firing nuclear weapons.

But West European governments, still struggling to cope with a protracted period of feeble economic growth, have balked at the higher spending required to raise the nuclear threshold.

Among NATO strategists, the new emphasis on conventional weaponry is designed to relieve anxiety about nuclear war by bringing non-nuclear forces to a level that, in effect, creates an alternative to the current nuclear balance of terror.

There are some Europeans, however, who argue that it is a strategy based on nuclear weapons that prevents the outbreak of hostilities by ultimately tying the United States to the defense of Europe. A strategy based on conventional forces, they argue, may not be the deterrent NATO strategists think it is and prove to be an invitation to a devastating conflict limited to Europe.

The depth of American frustration with the reluctance of European allies to invest more in their own military protection became evident earlier this year when Sen. Sam Nunn (D-Ga.) proposed a bill to bring home nearly one-third of the 326,000 U.S. troops in Europe unless the allies began doing more to boost NATO's conventional capabilities.

Although the bill was defeated by a vote of 55 to 41, European leaders were stunned. Nunn and several cosponsors are considered staunch advocates of the NATO alliance.

The shock of the Nunn bill has produced some movement in Western Europe to respond to the American complaints. NATO defense ministers are expected next month to endorse plans to spend $9 billion refurbishing military bridges, fuel depots and airbases over the next five years. In addition, West Germany and the Netherlands intend to step up purchases of more antitank missiles and artillery rounds.

But U.S. diplomats say they remain uncertain whether such measures will be sufficient to meet congressional demands.

At last week's meeting of the North Atlantic Assembly, which brought together 184 legislators from 16 NATO countries, Sen. William Roth (R-Del.) said that while he heard some "more positive talk" from the Europeans, he was still not satisfied with their commitment to accept heavier burdens in upgrading conventional defense.

"There will be great efforts in the U.S. to restrain defense spending to cut the budget deficit in the coming years," said Roth, one of the cosponsors of the Nunn bill. "It is very important for Europeans to understand the strong feeling in the United States that they should do more for their own good."

Roth said that Congress was developing a strong opinion that it did not make any sense to keep more than 300,000 American troops in Europe if they only would be able to fight for several days before nuclear war ensued.

"If U.S. soldiers are to serve only as a tripwire, their number is not so important," Roth said. "In South Korea, we only have one division to ensure our involvement." Roth contended that "the free world" possesses six times the wealth available to the Soviet Union and thus should be able to bear the necessary sacrifices for stronger defense.

In 1977, NATO countries pledged to boost their defense spending by 3 percent yearly after inflation in order to keep pace with the Warsaw Pact military buildup. But most European allies have failed to meet the goal since then. They blame the recession that has afflicted their economies in recent years.

Moreover, the poor prospects for growth during the rest of this decade have consigned European countries to the likelihood that defense spending will continue to be restricted.

A report by Karsten Voigt, foreign affairs spokesman of West Germany's Social Democratic Party, forecasts that European defense spending will grow by little more than 1 percent per year through 1990.

Among the major European allies, France and Britain intend to devote much of any increase in their defense budgets to modernizing and expanding their independent nuclear arsenals.

In West Germany, with the world's lowest birth rate for more than a decade, military budget increases are expected to focus on providing precious manpower.

Congressional action in coming years on U.S. troop levels in Europe will be determined not only by military facts on the ground, but also by the political risks of "destroying NATO in order to save it," as a West German legislator put it.