Any similarity between the Carter administration and the regime of a banana republic is, these days, not purely coincidental. As Washington returns to work after the summer doldrums, the crumbling of power has developed an inner momentum.

The whole world knows the president is weak. Interested parties inevitably press rival claims with heightened intensity. The administration thus becomes hooked on both horns of all dilemmas, and its insides come apart.

The financial community took the first bite. It has forced the administration to reverse its original policy of letting the dollar find its own level in trading against foreign currencies. Now the administration has pledged to support the dollar by keeping interest rates high at home. But with money rates thus immobilized, the administration has to rely almost entirely on budgetary policy (that is, taxes and expenditures) to manage the economy.

President Carter started the year hoping to hold the deficit in fiscal 1980 below $30 billion, and to achieve a balanced budget in fiscal 1981. The energy crisis has compromised those hopes already. Not only is there heavy government spending for a new program to produce synthetic fuels. But there is now the certainty of a recission, setting up new drains on the treasury from welfare and unemployment claimants. To avoid a truly horrendous deficit, the president has to get every little bit of the windfall profits tax he wants to impose on the oil companies. Even then, the deficit would be very large if the recession deepened and forced upon the administration the tax cut both Democrats and Republicans are readying to give a boost to the economy.

With his basic choices narrowly circumscribed by the twin scourges of inflation and recession, the president has almost no spare resources left for other issues. But the other issues keep coming along.

The Middle East looked like it was going away for a while after the Egyptian-Israeli peace treaty was signed early this year. All that was required was for the two parties to move through various stages prescribed in the treaty for the next year.

But the United Nations General Assembly beginning this month presented opportunities for a new drive on behalf of Palestinian rights. The Palestine Liberation Organization and its Arab backers tried to set the stage at sessions of the U.N. Security Council this summer.

The State Department Arbists and the Third World coalition lining up behind Ambassador Andrew Young thought they saw an opportunity for a genuine breakthrough. There followed an effort to engage the PLO, which led to bad blood with Israel, the resignation of Ambassador Young and a slanging match between blacks and Jews in this country.

The Strategic Arms Limitation Treaty has never been in danger of rejection by the Senate. But the weakness of the president ensures that he will have to pay a price for passage. Conservative Democrats and Republicans are insisting on a defense budget increase of from 3 to 5 percent.

That not only knocks another big hole in the hopes for a balanced budget; it also sets up new tension between liberals and conservatives in the president's own party. So Mr. Carter is going to be hard-pressed to win both the two-thirds majority necessary for passage of the treaty and the simple majority required for passage of the increased military budget.

Every one of these developments lines up partisans within the administration. The Treasury and the Office of Management and Budget are more interested in holding the line on spending than the Pentagon and the departments charged with social responsibilities. Ambassador Robert Strauss is jousting with Secretary of State Cyrus Vance and the national security adviser, Zbigniew Brzezinski, for control of Middle Eastern policy.

Maybe Jimmy Carter can assert mastery over this bewildering array of issues. But he has to do it soon -- before he starts losing political contests connected with the 1980 presidential campaign. Moreover, he cannot force the pace. Pressing hard only yields ludicrous events, like the crazy tale of an attack on the president by a furious rabbit -- the worst kind of event for a president in trouble, and the stuff of which are made banana republics.