President Reagan faces one of his biggest challenges as "the Great Communicator" this week as he tries to assure critics to the right and left of him that he is doing enough on national defense but not too much.

He will tell those on his right that he has, after several false starts, found a way to base the MX missile so it helps close that "window of vulnerability" he deplored so aggressively in his 1980 election campaign.

The president will also stress to those to his left that basing the MX does not mean the administration has given up on junking some nuclear weapons under an arms control agreement with the Soviets.

In fact, according to the Reagan argument, going ahead on the MX will make the Soviet Union more inclined to sign such a "we won't if you won't" agreement on deploying more doomsday weapons.

Reagan's record on strategic arms as he walks this rhetorical tightrope is vulnerable from right and left.

Critics on the right can charge accurately that Reagan, except for resurrecting the B1 bomber canceled by then President Carter, has done litte more on strategic weaponry than continue the Carter program of cruise missiles, Trident submarines and the Stealth bomber.

Reagan has ordered more cruise missiles and Tridents than Carter did, but he also has announced that he will reduce the nation's nuclear arsenal by retiring old B52D bombers and Titan blockbuster missiles, which Carter did not do.

The 10-warhead MX is not new with Reagan. Carter spent millions in getting the missile ready for production, and Reagan has continued the missile on course but scrapped Carter's plan for rotating it among cement garages in the valleys of Nevada and Utah.

Reagan, whose first idea of putting the MX in existing missile silos blew up on the pad in Congress, is expected to recommend tomorrow that 100 MXs be based in closely spaced columns on relatively small patches of real estate in the West.

The Air Force contends that these so-called "dense pack" formations would cause Soviet warheads to knock each other out. Those warheads, goes the argument, would be so bunched as they went after MX missile silos that one warhead could not explode without damaging others in the flock, or at least knocking them off course.

To make "dense pack" less vulnerable in the long term and easier to sell to skeptics in Congress and the scientific community, the Air Force has sent to Reagan through Defense Secretary Caspar W. Weinberger several options.

These include eventually protecting MX missile fields with updated antiballistic missiles and radar systems should there be no arms control agreement with Moscow. Other options are to bury some of 100 MX missiles deep underground in the south side of mountains or to build extra silos to try deceiving Soviet targeteers.

MX price tags have proved to be like stretch socks. About $4.5 billion has been spent on the MX, which has undergone about 30 variations in the Air Force. Deploying 100 MX missiles in dense pack formations would cost an additional $26 billion.

Even if Reagan's basing plan prevails over opposition in Congress and elsewhere, the first MX will not be deployed until 1986, long after he has finished his first term and perhaps left office.

So the president who decried the window of vulnerability will not be able to preside any time soon at a ceremony celebrating its closing.

His monument to making nuclear war less likely in his first term could be an arms control agreement with the Soviets. But prospects for that do not look bright. In the absence of an agreement in hand, Reagan is forced to stress how hard he is trying to obtain one while taking the hair-trigger off nuclear war.

His nationally broadcast speech tomorrow likely will stress his vigorous pursuit of arms control and, at least under several drafts of the speech submitted to him, call for a series of "confidence-building" measures to minimize the chance of the United States and Soviet Union going to war by accident.

The Joint Chiefs of Staff, told to come up with peaceful-looking gestures for possible inclusion in the speech, sent a proposal that both sides transfer money from nuclear to conventional forces.

A Pentagon civilian executive said verifying such a rechanneling of defense funds would be almost impossible.

Thought was also given during speech-drafting sessions to revealing more details about the administration arms control proposal being negotiated at Geneva in order to convince nuclear freeze advocates and others that Reagan is seriously attempting to slash superpower arsenals.

For the moment, however, Reagan is left with trying to portray himself as a president who, in the face of the Soviet military buildup, has no choice but to add missiles that he feels helps deter war while pursuing every avenue, including arms control, that promises to lead to peace.