Washington — President Reagan has a credibility problem on several fronts which may dominate the next three months before the fall election. What is unusual is not the intense national political review that has developed, but the extent and scope of the President's problems. They range from agriculture to banking, from tariffs to armaments, from the best way to balance the budget to the possibility of adding a new amendment to the Constitution.
Now Mr. Reagan has taken a quick trip out of the capital to Des Moines to test sentiment and tell the farm belt about his latest grain agreement with the Soviets. And before leaving Aug. 2 he had an intense interview with Israeli spokesmen over the Lebanon situation.
But much of the present-day Reagan problem grows out of a business revival that didn't come. For example, Treasury Secretary Donald T. Regan declared Jan. 6, 1981, ''If everything works well and nothing changes, we could see a balanced budget in the fourth year of the Reagan administration.'' But last month Mr. Regan agreed that ''this recession was much deeper than we thought it would be.'' Indeed, the Congressional Budget Office, through director Alice M. Rivlin, forecasts a fiscal 1983 federal deficit in the range of $140 billion to $160 billion for each of the next three fiscal years.
Most presidents have a midterm slump after two years; in fact no party in the White House has increased its representation in the lower chamber of the legislature at midterm since President Roosevelt did in 1934. How far can Reagan contain this normal decline?
Polls indicate that the President remains personally popular with voters. But there is a hint of sharper terms in the latest editorial comments on Reagan's record. For example, on the proposal for a constitutional amendment to ban federal deficits, the New York Times on Aug. 1 editorially condemns the plan as ''ignorant economics, destructive law, foolish administration, and cynical politics.'' On the tax front, the mass-circulation New York Post simultaneously warned on Aug. 2 that ''he stands in danger of forfeiting the basis of popular support for himself, his party, and for his program.''
Here are some of Reagan's other problems as he goes into the final three months before the midterm election:
* Relations with NATO allies. When Reagan returned from the Versailles summit , he seemed to have reached accord with America's Western allies. Shortly thereafter, however, Reagan announced his hard-line embargo against the European-Soviet pipeline, and angry cries have since filled the air. Critics charge inconsistency in opposing cooperation with the USSR by other democracies while selling American grain to the hungry Soviet with the approval of US farmers.
* China. There is a parallel criticism of the US simultaneously from communist China, which denounces the proposed US deal with anticommunist Taiwan to continue selling it arms. The Chinese say a crisis with America impends in what they denounce as a ''policy of intervention in China's internal affairs.''
* Economic program. President Reagan began his incumbency with a promise to meet economic problems with ''supply-side economics.'' A quick, sharp cut in taxes, he hoped, would stimulate the economy and perhaps bring in larger revenue than it cost. He also asked new defense expenditures and consolidation of some relief spending. Little is heard of the plan anymore in Washington. As to business revival, the Dow Jones average, often used as an investment scale, reached above 1000 early in the Reagan administration, but is now around 820.
* Strain within the administration. The most conspicuous upset in the Reagan domestic family was the departure of Alexander M. Haig Jr. as secretary of state. But this was only one in the steady attrition that has continued in Reagan's second year. A similar development has gone on on the domestic front. For example, Murray L. Weidenbaum, chairman of the Council of Economic Advisers, decided to drop out of the office. Although he denied that ideological differences caused the departure, the resignation appeared to spring from frustration in the failure to shape events.
* Economics. The biggest domestic issue in Washington is over the recession and what to do about it. The critical question at midterm often is, ''Are you better off today than when the President took office?'' President Reagan's standing on the opinion polls has come down substantially as the recession has continued and unemployment has remained at about 9.5 percent.