Asserting that a Democrat cannot win the White House without winning in the South, Democratic governors from the region, led by Florida Gov. Robert Graham, are pushing to have southern states hold primaries on the same day.

Sponsors of the idea say that giving southern states a greater role in delegate selection would increase the South's influence over the process and increase the chances of a Democratic victory in the general election.

The southern states select about one-third of Democratic delegates. Such a change could alter the outcome of the 1988 race by dwarfing the influence of the northeastern states and by helping more conservative candidates, experts say.

Meeting here at the Southern Governors' Conference, the governors and state legislators named a task force to work on the effort.

Texas State Sen. John Traeger, chairman of the Southern Legislative Conference, said the group hopes to get as many as 10 southern states to agree to hold their primary or caucus on the same day.

Texas Gov. Mark White, complaining about the effect of early primaries on the later-electing states, charged that "the Democratic Party is warped by the timing of the procedure. Many candidates who would have done well in Texas were already out. We are tired of getting leftovers."

He said it is likely Texas will move up the date of its delegate selection, and he favors changing Saturday caucuses to a Tuesday primary.

Graham painted a picture of a futile candidate who must sell himself to special-interest groups across the country to fund his campaign in all the states.

He said, "The current system has lived up to its expectations. We have maximized the influence of permanent special interest and diminished the influence of mainstream party members. The candidate ends up selling his soul across the country. By the nomination there is no soul left to give the country."

Graham said the ideal would be for 75 percent of southeastern delegates to be chosen on the same day in early March.

Central to his proposal is for Texas, which chooses 200 delegates, to join Florida, Georgia and Alabama in selecting delegates on "Super Tuesday," the second Tuesday in March. If Texas moves up the date, Oklahoma and North Carolina are considered likely join the trend.

Graham expects strong opposition from the Democratic National Committee but can achieve a common primary if southern legislatures agree. Most meet in 1986 and most are controlled by the Democrats, improving chances of this proposal, which is considered a long-shot effort.