President Bush has issued orders to Secretary of State James A. Baker III to break the U.S.-Soviet nuclear arms deadlock, but the United States faces an uphill climb against the political and economic turbulence tearing the Soviet Union apart and threatening to bring down Mikhail Gorbachev.

It became clear during private sessions here this week between U.S. and Soviet officials that chances of resolving two tough issues before the November election are bleaker than ever before. Baker's arms control team struggled without much hope to find a formula for overriding confusion on the Soviet side. Starting today, Baker tries again with the first of several negotiating sessions on START with Soviet Foreign Minister Eduard Shevardnadze at the United Nations.

The collapse of progress toward Bush's long-promised 1990 strategic arms control treaty (START) shows the growing political power of the Soviet military. It also demonstrates that Gorbachev heads a phantom government, powerless to fend off the demands either of his military or of independence-minded nationalists.

In the case of START and arms control, the political victim would be George Bush, not Gorbachev. For nearly two years of highly successful negotiations with Gorbachev, Bush has based his policy on this promise: a START treaty by the end of 1990 that would make big cuts in the Soviets' large SS-18 strategic nuclear missile, from 308 down to 154.

Soviet generals are simply not buying. It is not clear whether they truly are alarmed by the huge American military buildup in the Persian Gulf, as a few administration specialists claim, or Soviet generals are like other generals in not ever wanting to cut their arms. What is clear is that with the old, centralized Communist command structure withering away, Soviet generals can say "nyet" to Gorbachev and make it stick.

The other major barrier to Bush's promised START treaty is hardened Soviet resistance to an agreement between Bush and British Prime Minister Margaret Thatcher. The United States has pledged to arm three planned British Triton submarines with the super-accurate D-5 Triton II missile. The Soviet generals are arguing that this amounts to "circumvention" -- using British boats to replace American boats.

The problem is worsened for Bush by the fact that he and Baker dare not jeopardize Gorbachev's cooperation with the U.S. Persian Gulf buildup by forcing him to the wall on START. But State Department officials are telling the White House that failure to fulfill this promise will cost at the polls Nov. 6.

The deadlock on arms control suggests the grave costs of Gorbachev's power outage, evident in other areas -- particularly in dealing with Russian Republic President Boris Yeltsin.

Using the presidential-decree powers he got last March, Gorbachev ordered a $5 billion deal with the South African mining giant deBeers to market Soviet diamonds. The independent Russian parliament, on the request of Yeltsin, immediately declared Gorbachev's decree "null and void." It claimed that since most of the diamonds are extracted from Russian territory in Yakut, on the far rim of Siberia, their disposition was under the control of Russia, not the Soviet Union.

Gorbachev reacted by getting the Soviet parliament to rule the Russian action equally "null and void." The Russian parliament then again condemned the Soviet parliament. Here was no Marx Brothers comedy but a graphic example of government in chaos.

If a mere $5 billion deal with deBeers was beyond Gorbachev's ability to sell Yeltsin, it is little wonder that, with its higher stakes, selling START to the generals might also come a cropper.

With Gorbachev fighting for mere survival and with predictions of food riots in Moscow this winter, arms control is clearly far down on his agenda. Dealing with a phantom Soviet government was hardly Bush's expectation nearly two years when he put all his chips on START. Now that it has come to pass, what seemed then to be a sure campaign asset is turning sour.