The Democratic convention displays the Carter machine in action. What foiled the challenge of Sen. Edward Kennedy is a network of connections that dispenses federal patronage to Carter supporters among state, county and local officials. But while that structure packs power within the Democratic Party, it does not lend itself to the framing of the broad social and economic policies required to reach the country as a whole.

Like most things in politics, the Carter Machine came into being largely by accident. President Carter arrived in Washington with a commitment to make the federal bureaucracy responsive to local needs. To that end, he fused two previously separate White House functions in a single person.

Jack Watson, an attractive, Havard-trained lawyer from Atlanta, became both secretary to the Cabinet and assistant to the president for inter-governmental relations. Watson, when he succeeded Hamilton Jordan as White House chief of staff in June, passed on both hats to his deputy, Gene Eidenberg.

At the outset, Watson had to reach for what he could find. To establish himself with the Cabinet, he created a corps of departmental operators -- assistant secretaries and special assistants who had operational control over programs in the field. To make himself felt in the country, he began cultivating the more than 6,000 officials who filed the top spots as mayors, county commissioners and governors.

"We listened to their problems," Watson recalled in an interview the other day. "We told them in advance about our plans. Over time, we became friends, good friends, intimate friends."

As intimacy developed, Watson realized there were all kinds of favors he could do for local officials. They began to appreciate his help. Over time, he became the chief White House personnel officer -- closely connected for example, with the selection of Moon Landrieu, former mayor of New Orleans, as secretary of housing and urban development; and of Neil Goldschmidt, former mayor of Portland, Ore., as secretary of transportation. There thus grew up, in an era of open government and reform and during a time when the fix was out, a legitimate way for systematically squeezing patronage from the welfare state for a clientele of local officials.

Examples abound. Gov. Bob Graham of Florida, who is due to place the presidents's name in nomination, was given, from funds usually reserved for natural disaster, money to take care of the wave of Cuban refugees who came to Florida last winter. Lynn Cutler, a commissioner in Black Hawk County, who helped vitally in the Iowa caucuses, was given grants that enabled a meat-packing plant in Waterloo to stay open. Mayor Tom Bradley of Los Angeles, probably Carter's leading supporter in California, won federal aid for a new highway -- the Century Freeway.

The test came when Kennedy announced his candidacy last fall. Many persons, including the senator himself, seemed to think that his declaration would set in motion a surge of support. But the Carter network held. The president maintained the loyalty of the vast majortiy of Democratic governors, county commissioners and mayors all over the country. Since then, with their help, he has been out front all the way.

Despite its impact on the party, however, the Carter machine has distinct limitations. It is the work of newcomers and outsiders. The best they can do in power is to squeeze the bureaucracy for a few, relatively meager favors.

But to this day, the Carterites have not mastered government. Their relations with Congress are in tatters. They have yet to surface a major social program. It is typical that, although they have the majority here, they are on the defensive with regard to the platform. They are divided on economic policy -- even on the content of the program for revitalizing American industry that will presumably lie at the heart of the president's campaign.

The cantrast between doing favors and devising broad approaches defines Carter's political problem. The president can win renomination by servicing the network of Democratic officeholders.

But winning reelection requires imparting to the country as a whole a sense of hope for the '80s, a vision of America. It requires clear-cut approaches to fundamental problems. If he is to win the campaign that begins when this convention ends, Carter has to show that he can go beyond personalizing power -- that he stands for something besides himself.