NASHVILLE, JUNE 17 -- As Joe Sensenbrenner, the Democratic mayor of Madison, Wis., watched a parade of six presidential candidates discuss homelessness, poverty and teen-age pregnancy, he was struck by the thought that "this is not what the people in the bars and supermarkets are worrying about."

For most Americans, Sensenbrenner contended, "The problems we are most concerned about are not part of their daily experience. In the view of many Americans, the cities are in better shape than they were five or six years ago."

Sensenbrenner's comments reflect two of the central problems facing Democratic presidential candidates that emerged from the five days of the 55th annual Conference of U.S. Mayors, an event planned to showcase the competitors for both parties' nominations:The experiences of many cities under the Reagan administration -- particularly the cities in the hard-core Democratic terrain of the nation's East Coast -- have been an ambiguous mixture of blossoming downtowns and gentrified slums combined with sustained poverty, housing costs that have risen faster than income and homeless people wandering the streets.

"That is the great dilemma for the Democrats: how to speak to the possessed and the dispossessed at the same time," said Arkansas Gov. Bill Clinton (D), who remains undecided whether to attempt to find a political voice to overcome that dilemma and run for the presidency. The administration's economic policies -- particularly the creation of over $2 trillion in federal debt -- have severely constricted the ability of Democratic candidates to campaign among their most loyal constitutents, the elected officials and voters of America's cities.

Repeatedly, Democratic presidential candidates were forced to present complex and politically conflicting messages to the mayors.

Take, for example, the case of Rep. Richard A. Gephardt (D-Mo.). On one hand, he described a growth of urban poverty "because our society has yet to address and conquer the problems of illiteracy, high school dropouts, disease, teen-age pregnancy, malnutrition, drug dependency, alcohol abuse, family violence and most of the things that kill the dignity and hope of human beings."

At the same time, he told the mayors "the Reagan years . . . have left us with a limited range of choices. So let me be quite frank. We cannot put the nation back on a safe and sure course for the 1990s and beyond the year 2000 without imposing discipline on the federal budget process."

Even Jesse L. Jackson, the most liberal of the Democratic hopefuls, has been forced by the politics of the budget to say:

"Let us be candid with one another. As much as I would like to, I cannot promise that the next president of the United States will unlock the safe to find billions of dollars which should have been accumulating to the cities' accounts of the last seven years. The sad, true facts of our national deficits are well known."

For Democratic presidential candidates, these political-economic tensions function to pit the interests of the most loyal party supporters -- the urban poor and working class, two key groups in the primary-election process -- against the swing voters of the middle class, a group that turns out in much higher percentages in general elections.

One of the "last things Democrats can afford to do," Clinton said, is to let the public think: " 'Here they {the Democrats} go again. They are going to cost us income.' "

In private, a number of the 200 mayors here acknowledged that none of the Democratic candidates has found a way to master the dilemma defined this way by Clinton: "The budget straitjacket we've gotten ourselves into and the economic uncertainties of the years ahead make it impossible for a responsible person to commit {specific amounts of money} as president for certain programs . . . . That is one of the legacies of the last seven years."