You could not watch the Democatic convention without sensing that the delegates felt themselves the doomed stragglers in history's wagon train.

There is more to this than President Carter's low popularity. The delegates' nostalgic recollection of Franklin D. Roosevelt and Harry S. Truman betrayed their fears that the great coalition built by these giants finally is crumbling beyond repair.

What is important about this election is that, for the first time since 1960, it is being fought largely on economic issues. This orientation has exposed the Democratis' soft underbelly. All parties must appeal for support on two levels -- to the electorate at large and to specific constituencies -- and the Democrats now find it increasingly difficult to reconcile appeals to the middle class and to the traditional constituences of the poor and disadvantaged. If Carter cannot surmount this problem, his defeat may end 50 years of Democratic surpremacy.

Rash as this prediction seems -- and is -- it simply reflects the magnitude of the pressures on the Democratic majority. Strong corrosive forces already are eating at the party's foundations. The generation that lived through the Depression and World War II is aging and fading in importance, replaced by the post-war "baby boom." These voters have diminished party loyalties and rightly or wrongly, increasingly regard themselves as middle class. As they age, they are likely to become more cautious and selfish -- less willing to make sacrifices for traditional Democratic constituencies.

A recent study by two political scientists makes clear the nature of the problem. In a fascinating analysis of the unemployed ("Injury to Insult, Unemployment, Class and Political Response," Harvard University Press, 1979), Kay Lehman Scholzman and Sidney Verba find that the jobless are not particularly politically active.

In effect, the political pressure for lower unemployment has depended primarily on the good will and commitment of the employed. But as these groups encounter their own economic problems -- inflation and squeezed living standards -- they may quietly tolerate higher joblessness.

This simple insight, which probably applies to many other programs for the poor as well, explains much of the Democrats' turmoil. The party's whole moral purpose consists of helping the poor and disadvantaged, and yet the political wisdom of this emphasis increasingly stands threatened. The tension is pervasive. It constituted the contested terrain between Carter and Sen. Edward M. Kennedy and caused much of the confusion and inconsistency of Carter's first term.

The genius of Roosevelt -- and the power of his legacy -- was his ability to marry a mass appeal with the loyalty of specific constituencies. His programs did not dispel the Depression (World War II did that), but his long reign identified the Democrats as the party of prosperity. Moreover, his enthusiastic support of government economic interventionism invited the allegiance of all those groups that felt oppressed by the unfettered operation of the private economy.

All this left the Republicans with precious little. Their economic constituency consisted largely of those -- mainly the upper middle class -- who felt economically secure. And their broader appeal rested on a reputation of being more "responsible" in foreign affairs and, in general, more honest. Such assets sometimes sufficed to secure the White House but not to make much headway in Congress or state legislatures. And Richard M. Nixon smudged even the Republicans' good name.

Economic changes now have battered these convenient stereotypes. Unemployment is 7.8 percent, and the Deomcrats, obviously, are no longer the certain guardians of prosperity. The squeeze on the budget has reduced their ability to satisfy individual constituencies, and the effort to break inflation compounds the difficulty of either increasing spending or reducing joblessness.

Carter is now surely aware of the basic tension in the Democrats' heritage.

His recent emphasis on economic "renewal" and reindustralization aims at combining programs that satisfy specific constituencies with an over-all theme of prosperity. He is seeking to modernize the Democratic coalition as much as the economy. Meanwhile, he simply hopes to discredit Reagan and the Republicans by questioning their sincerity and branding their tax proposal inflationary.

Possibly he can succeed. The turn in Republican rhetoric toward tax cuts and job creation is so startling as to invite ridicule. But the actual differences between the two parties, exaggerated by campaign rhetoric and journalistic hype, are small: The Republican tax-cut proposal is $36 billion, and the Democratic Congress is likely to pass something close to $30 billion.

Should Carter lose the election, the Democrats could be in trouble. The pattern of politics over the past two decades is that the "out" party that wins the White House swings toward the middle and the incumbent party that losses swings toward its ideological extremity: In 1964, the Republicans nominated Barry Goldwater; in 1972, the Democrats, George McGovern; in 1980, the Republicans, Reagan.

This could prove dangerous. For, if the Democrats are to reemphasize their New Deal roots and commitment to social programs -- what Kennedy urged on the convention -- they are implicity counting on an austere economy to revive class consciousness and make people identify with their cause.

But, in fact, class consciousness never had been strong and is diminishing. One survey cited by Schlozman and Verba, for example indicated that respondents identifying themselves as upper or middle class increased from 51 percent in 1939 to 67 percent in 1976, and those classifying themselves as working class declined from 16 percent to 4 percent.

The Republicans seem acutely aware of this. What distinguished the Republican from the Democratic convention was the unabashed emphasis on the middle-class values and success -- and the old American Dream. Scholzman and Verba find belief in this ideal still strong. Nothing is certain in politics to become polarized, their majority status could disappear.

The GOP might not replace them, but the political balance could become genuinely precarious.