Mr. Reagan's political dilemma

President Reagan went ''the last mile'' up Capitol Hill in Washington last week in what purported to be a decisive effort to work out a bipartisan agreement on a budget for the United States for the upcoming fiscal year.

He could have had agreement had he been willing to give up the third year of his three-year tax cutting plan.

He would also have pleased most of the leaders of his own Republican Party who are getting increasingly anxious about the effect on the party's prospects in the November elections of big budget deficits and of the high interest rates which are bred by the deficits.

He refused to give up the third round of his tax cuts, thereby producing forecasts of a federal deficit of $182 billion for 1983 and of deficits running well over $200 billion by 1985.

Mr. Reagan has another way of trimming down those prospective deficits and getting himself back into line with his own 1980 campaign promises. He could trim back on his defense program - which most experts say is well beyond the sums which the Pentagon can spend prudently and efficiently. It is also above what some (though not all) foreign policy experts think is justified by the actual world situation and the real military balance between the US and the USSR.

The nub of the argument is over whether the Soviet Union does in fact have that ''definite margin of superiority'' over the US in strategic weapons which the President has asserted.

If Moscow in fact has such a ''margin'' and if there therefore is a real ''window of vulnerability'' through which Moscow can expect to gain important advantages in power politics over the US and its allies -- then the case for the big defense budget is solid and unassailable.

But is it?

You, the average reader, and I, the reporter, cannot know where the truth lies. The subject is too technical for the average reader to grasp or the average reporter to expound. But in case you want to try to wade through the technology of the subject I offer here what is probably the most authoritative statement to be found in the technical journals on the subject.

This comes from the latest ''Strategic Survey,'' an annual publicaton of the International Institute of Strategic Studies. See if you can understand it.

''. . . the vulnerability of US ICBM is much more a theoretical than an operational concern. To destroy the 1,064 US ICBM silos, the Soviet Union would need to use some 2,000 perfectly coordinated warheads -- including a second (and perhaps even a third) wave to compensate for failures in flight and on detonation in the first wave -- all of them spaced and timed to avoid mutual destruction by the phenomenon known as 'fratricide' which can cause the nuclear explosions of some warheads to affect other warheads before detonation. The command and control requirements of such coordination border on the infeasible. Moreover, the United States could avoid the destruction of her ICBM force by recourse to tactical measures such as launch-on-warning (LOW) or launch-under-attack (LUA), which would leave only empty silos for incoming Soviet warheads to destroy. At the very least, the possibility of LOW or LUA tactics could deter the Soviet Union from undertaking a counter-ICBM attack in the first place. . . .

''Therefore, if the Soviet Union were able to make political gains during the period of the 'window of vulnerability,' this would not be because of any objective strategic balance in her favor, but, rather, because the limited perspectives of the American strategic debate had led to an underestima-tion of the conditions of nuclear deterrence and of US capabilities.''

In other words talk in Washington about US inferiority could give the Soviets opportunities for exploitation which the actual strategic situation does not justify.

But if Mr. Reagan changed his position and rejected the doctrine of US inferiority he would pull the rug out from under his defense budget.

That doctrine of inferiority is the rationale for the military budget just as surely as the doctrine of supply-side economics is the rationale for the tax cuts.

Mr. Reagan's political dilemma is that he is headed straight into the worst peacetime deficits in all history unless he can give up the rationales for his tax cuts and his big defense budgets. But to give up those would be to abandon the constituencies which put up much of funds for the 1980 campaign and are ready, presumably, to continue to fund Mr. Reagan's political future.