Mayor Gerald Blessey, who dined with Walter F. Mondale two Sundays ago and lunched with Sen. John Glenn (D-Ohio) on Wednesday, holds a couple of political truths to be self-evident:

One: "John Glenn would be the easiest candidate to sell in my area--because of his astronaut and military records."

Two: "We'll carry Biloxi for Fritz Mondale in the caucus . . . . We can deliver it."

The mayor of this Gulf Coast city where right-wing Republican Trent Lott is the congressman and the Jefferson Davis Shrine is just down the road, has decided to commit himself to Mondale for president in 1984. He said he was impressed with both candidates at the meals at the governor's mansion in Jackson last week: Glenn seemed sincere and capable, Mondale addressed the issues in greater detail.

But Blessey came to his decision more than a month ago, when Mondale called to talk about issues and experiences and ask for his support. Blessey had not heard before or since from Glenn or any of the other Democratic presidential candidates.

That is the sort of move that can make a difference, as Mondale strives to lock up the nomination early by making inroads in the southern constituency that would not appear to be naturally his. The South will have more delegates in 1984 than ever before, and its caucuses and primaries are earlier than ever before.

Politicians across the South tell tales similar to Blessey's: that Mondale has made every effort while they haven't heard from Glenn.

Mondale and Glenn are the two non-southerners in the race whose plans include making a full-court press in the South.

Sen. Alan Cranston (Calif.) is working hard in just one southern state, Alabama, in the hopes of demonstrating a nationwide base for his liberal candidacy.

Sen. Gary Hart (Colo.) is preparing for a modest showing in the South.

Sen. Ernest F. Hollings (S.C.) and former governor Reubin Askew of Florida have the potential to do well in the region, but their candidacies so far are considered strong only in their home states.

Glenn's potential in the South seems to be everywhere; his organization seems to be nowhere. His strategy is built on a southern base, yet his campaign has no southern coordinator.

As an American hero, he was the candidate most in demand at Georgia's mammoth Democratic Party gala last week. Georgians streamed into his crowded reception asking his aides for "Glenn" buttons for souvenirs, but the Glenn people had to confess that they had brought none.

The contrast between the two early front-runners can be seen in the way they deal with Gov. Robert Graham of Florida. He is out front now for Askew's long-shot candidacy, but he said he gets a courtesy call from Mondale every time the former vice president comes into the state. Glenn, he said, has made several visits, but has never called.

Organization is especially important in caucus states such as Mississippi, where the right staff can be more important than the right stuff.

"Glenn could probably win here if we had a primary," said Biloxi's Mayor Blessey, a moderate and practical man. "But in a caucus state it becomes an organization problem. That's why I say we can carry it for Mondale . . . . But he has to shed some of that baggage of the past--he has to convince people he is not going to reinstate large-spending social programs."

A sedan with Georgia plates rolled up to the Mississippi governor's mansion, and the driver unpacked his charts and tripod stand from the trunk of the car. Hamilton Jordan's Traveling Political Science Show had arrived.

One by one, Jordan has been making the rounds of the southern governors, putting on a one-man lecture, complete with visual aids, to convince them that the Democratic presidential candidate needs the South to win the general election--and that it is up to the South to keep the candidates in the political center.

"When I started going around, people thought Jimmy Carter was going to hop out of the trunk of my car and start handing out brochures," Jordan said. "But I don't have any agenda."

What Jordan does have is a crusade, pushing the message that history shows that Democrats cannot get elected in general presidential elections without the South. Moreover, this year the South is even more important, because the calendar is loaded with early southern primaries and caucuses.

After the Iowa caucus on Feb. 28 and the New Hampshire primary on March 6, comes a week in which 16 state contests are tentatively scheduled, seven of them in the South: the Alabama, Florida and Georgia primaries (287 delegates) and the Arkansas, Mississippi, South Carolina and Tennessee caucuses (243 delegates). They account for almost 14 percent of the Democrats' total of 3,923 delegates.

"I'm just trying to create an awareness," said Jordan. "I'm saying we must wake up to how important we are and the influence we have . . . . If you have a muscle and you don't use it, it's like you don't have it. So I'm saying get close to some candidate. Push him. Get him to adopt centrist positions."

As the candidates sweep through the South, they campaign as solid centrists all, hugging the middle of the road. Mondale talked mainly about family and farms and being a preacher's son, and wooed the folks in Hawkinsville, Ga., by referring to a menial farm job he held as a boy in rural Minnesota:

"I'm the only licensed pea lice inspector ever to be elected vice president of the United States."

In Mississippi last week Mondale basked in reflected moderation when Gov. William F. Winter introduced him as "a mainstream politician" and a man of "mainstream heartland leadership."

Winter, a highly regarded moderate who had listened with interest not long ago to Jordan's case, is neutral, but leaning toward Mondale. He is publicly uncommitted, but he assembled the list of prominent Mississippians who were invited to dinner with him and Mondale and is considering an offer to play a prominent role in the Mondale campaign.

But he is trying to be evenhanded. So when he heard that Glenn was coming to town to address the legislature, even though the Glenn campaign never contacted him to tell him about it, he offered to set up a luncheon for Glenn.

And he introduced Glenn at the capitol in glowing terms as "a person on whom this country could rely in any situation for the determination, the vision, the courage to see us through . . . . "

Glenn scores well all over the South. The Mississippi legislators warmly praised what they had heard and the character of the speaker.

Mondale gets no hero's welcome. His prospects lie to a significant degree in the potential of the black vote.

So, in Atlanta, he appealed with passion for black support, reminding the blacks repeatedly of how he had supported every one of their causes for two decades. Most of those in the meeting were receptive, saying they were willing to overlook the fact that he had not supported the black Chicago candidate, Rep. Harold Washington (D-Ill.), who won the mayoral primary there.

Mondale's and Glenn's prospects in the South are tied, in part, to Askew's performance in Iowa and New Hampshire, because that could be the key to Florida's 143 delegates.

"If the primary in Florida were held today, Askew would win going away," Graham said in an interview last week. "But the question for 1984 will be how Floridians see the Askew campaign then. If he is not perceived by them as a viable national candidate, based on his showings in the early straw polls and caucuses, then the race in Florida will be much, much closer."

Although Askew was a strong and highly respected governor, he has kept a low profile in the state since leaving office in 1977. Also, officials estimate that one-third of the voters in 1984 will have become eligible to vote since Askew last appeared on a Florida ballot.

Mondale has his own southern connection, but he doesn't always remember to mention it. In Atlanta, at last week's candidate "cattle show," in the same complex where the Carter-Mondale team accepted victory accolades in 1976, Mondale was the only presidential aspirant who never once mentioned the name of Jimmy Carter.

"It was totally unconscious," said campaign press secretary Maxine Isaacs. "He didn't mean to omit President Carter. He was just thinking about making his own case."