Gen. Alexander Haig's quest for the 1988 Republican presidential nomination continues to be an enigma wrapped in media obscurity but kept alive by an enduring third place in the polls. Sometimes he polls a few points ahead of New York's Rep. Jack Kemp, leaving Kemp in fourth. Sometimes he falls a few points behind. So put him and Kemp in a tie for third; but if Kemp is a real politico, what is Haig?

A few weeks ago he put in a notable showing at the Midwestern Leadership Conference, attracting Republican foot soldiers. Within hours a New York Times/CBS News Poll gave him the second highest approval rating of Republican presidential contenders from probable Republican primary voters, but still his candidacy remains a mystery.

Haig is a military man. He was a general -- the supreme allied commander in Europe, and a very good one. He is a competent manager, having served as chief of staff for presidents Nixon and Ford during the Democrats' last days of investigative glory. Recognizing Haig's stature abroad, especially in Europe, Ronald Reagan made him his first secretary of state. Haig is keenly proud of his decades of experience at the center of government, but the fact is that the bulk of his experience has been in the military, and military men are very odd politicians.

Most of them sniff haughtily down at politicians. Even when placed in political positions, they disdain the pols. De Gaulle certainly did, and so too Eisenhower, whose temper tantrums against them were colossal. Ike judged the politicians' rituals infantile. Their practices made him impatient. He had no time for their vacuous schmoozing or any of their other time-consuming folderol. But Haig is odd even for a military man. He seems to like politics -- he will not admit it, but he does.

Admittedly the contempt that most military men hold for politics is self-delusory. Men like De Gaulle and Eisenhower were pols to the tips of their fingers. Neither was a great field commander as was Grant. Rather their forte was acquired power, through the ranks at first, in civilian politics later. Still, when it came to electoral politics they were impatient with the ritual. Haig is not.

He thumps his chest to crowds large and small as he declaims on his vast experience in government. From the row over Suez in 1956 to his retirement from the State Department, he crows that he has been nearby through every major crisis involving the United States. He is not saying that he was nearby merely because he is a military man. He is stressing his management skills and his talent for strategic thought.

This is a political package that other military men rarely confect. Haig has a political mind, which is not surprising. He follows the great game of politics with an avidity reminiscent of his old mentor Richard Nixon. His present campaign demonstrates his inability to wage the kind of rambunctious campaign that Nixon would run, but he stands for the same kind of big themes, stressing geopolitics, the international economic condition, trade, peace.

Possibly I put my finger on the key to the Haig mystery while reading Eugene McCarthy's latest tome, ''Up 'Til Now.'' There are in politics certain figures who embody a political party's fundamental values. They are the innocent carriers not of the party's oratorical blah but of at least some of its fundamental values. McCarthy represented the Democrats' desire to disengage from world politics and to settle into a cocoon of bogus intellectualizing: introspection, alienation, gimcrack poetry. In 1968 Eugene McCarthy went off willy-nilly along the campaign trail, spouting existential pieties packaged for Americans. Those were the emerging values of the Democratic Party, as Sen. Joseph Biden is about to demonstrate.

Today as Haig speaks of his managerial competence, his geopolitical grasp, his knowledge of international economics, he is embodying values that are at the heart of his party. Arguably they are the future of his party. The question is can Haig bring them into the White House or are they just a bit beyond the ken of the average voter, as McCarthy's values were? If they are, what does that tell us about the future of the Republican Party?