The Republicans came here to Detroit to broaden the base of their party. But did they? So far, at least, the answer has to be: not much, if at all.

Urban America, symbolized by this city, was one obvious target for Republican growth. By fostering inflation, the Carter administration has caused a net decrease in the take-home pay of working people. It has had to fight inflation by unemployment with further adverse impact on working people -- especially in big industrial cities such as Detroit.

The Republicans haven't deliberately slapped urban American in the face. But they didn't have to, given their attitude on budget matters.

At present, there shapes up a deficit of over $50 billion in this fiscal year alone. The Republicans have promised to balance the budget. They have also promised tax cuts of about $30 billion and an increase in defense spending of at least $10 billion. That leaves a deficit of $90 billion to wipe out.

How will it be wiped out? Almost certainly by cuts in subsidies for housing, health, urban transportation, education and the other services that make urban life bearable. So it will be very surprising if the major urban centers now turn toward the Republican Party.

A second constituency open to appeal comprises that growing number of Americans affected by what has been called the "post-materialist" values. Those are people not primarily concerned about either economic or physical security. They have been more interested in finding satisfaction through an interesting job or a voice in the affairs of their community.

That group has been put off by Jimmy Carter's turn to the right on such matters as national defense and energy policy. It would have liked to go Republican, and the party made a step in its direction by stress on the quality of life.

But to the Americans interested in newer values, the stance of the Republican Party on abortion and women's rights builds a critical barrier. The party is not saying yes to the future of the so-called social issues. It is deliberately reverting to a nostalgic past, and it is unlikely to fare well with younger Americans looking for a place to go.

Finally, there are those of us mainly concerned by the arthritis of economic institutions that threatens this country with slow death. We have been worried by the decline of basic industries, including autos and steel. We have seen in the failure to make rapid adjustments a major cause of both slow economic growth and ongoing inflation.

To those conditions we have traced the present imbalance in both this country's internal and external position. On the one hand, there is the increasing poverty of the major northern cities dependent on the older heavy industry, as against the growing wealth of the Sun Belt cities. On the other hand, there is the decline of the United States in the world, particularly with respect to other countries that have proved more adaptable to changing conditions -- notably West Germany and Japan.

In theory, the Republicans were the right party to deal with the slow death problem. They are supposedly the party of enterprise. More important, they are not tied to the ethnic minorities or trade unions or local governments that tend to fight change.

But for those who look to the Republicans as the angel of progress, the convention has been at best disappointing. The party has shown, by its stand on the social issues, reluctance to face the future. The platform stresses free enterprise in a blind, old-fashioned sense.

Worse still is the adversary stance respecting government. Reagan himself, and every other speaker of note, have shown hostility toward federal authority. The platform slaps government and vaunts "smaller communities, such as the family, the neighborhood and the work place."

Unfortunately, however, the "family, the neighborhood and the work place" cannot organize the revitalization of American institutions. They cannot promote the new industries that have to be advanced, nor ease out the old ones that need to be contracted. Least of all can they augment this country's strength in the world community.

Action to that effect requires decision in one place -- creative government. By denying government a critical role in restoring vitality in the country, the Republican deny reality. They show themselves again as stand-patters dominated by outworn shibboleths. They make it very hard for progressives who have had it with Jimmy Carter because of his "small is better" approach.

To be sure, the inability of the Republican Party to broaden support is not definitive. Many Democrats remain disaffected and open to appeal. But if it comes at all, the appeal will have to be made over the body of the party, in the person of Reagan himself.