They're holding a mayoral election here Tuesday, but the poo-bahs of the Democratic Party are afraid nobody will come.

To be more precise, Cook County Democratic party Chairman George Dunne is afraid not enough voters will turn out.

The election, to fill out the unexpired portion of the late Richard Daley's term, is not in doubt. Acting Mayor Michael Bilandic, who succeeded to the fifth floor of City Hall upon Mayor Daley's death last December, will easily triumph over Dennis Block, the Jone Republican in the 50-member City Council.

Eve the margin of Bilandie's victory is no cause for concern.

What worries Dunne is how many people won't turn out for the election at all.

Recently Dunne hosted a pep rally for a couple hundred precinct captains, the party stalwarts whose loyalty, and often their jobs, is determined by the number of votes they can turn out in an election.

When Richard J. Daley led these rallies the precinct captains would charge out the banquet hall without finishing their second cup of coffee in their zeal to turn out the vote.

But Bilandic is no Daley. It's difficult to rally the troops around the acting mayor's favorite phrase from his campaign speeches: "I'm not a politician. I'm an administrator."

When the rally ended, and the captains began shuffling for the exits Dunne sensed the danger and called them back. His message: "There's never been a mayoral election in this city with a turnout of less than 45 per cent. The primary turnout [in which Bilandic outpolled five also rans] was only 47 per cent." Victory alone isn't sufficient, he warned them. A mandate is needed. "The pundits will be quick to point out to the city and to the nation that invincibility of the Democratic Party has dissipated," Dunne concluded.

The "pundits" said the party was faltering last December, when Daley died leaving no heir apparent. Six claimants stepped forward to vie for the mayoral nomination in the April 19 primary. But the party closed ranks behind the 55-year-old Bilandic, a bachelor, a lawyer and the alderman for Daley's home 11th Ward, the most powerful and patronage-heavy in the city.

There were plenty of soft spots in Bilandic's primary victory, however. He won with a mere 50.38 per cent of the vote, and in 29 wards, the creaky Democratic machine failed to muster more than half the votes for the party's designated standard-bearer.

Many party chiefs are convinced that that lackluster showing has disqualified Bilandic for slating in 1979 to run for his own term. If Bilandic hopes to prove himself worthy of running for a full term he will have to win big on Tuesday, and the turnout will have to exceed at least half the eligible voters.

But Bilandic isn't the only one running against himself. His challenger, Alderman Block, faces the same task.

Block, a 29-year-old Chicago-born attorney who reluctantly allowed himself to be pressed into running after half a dozen other Republicans refused to sacrifice themselves, is running primarily against the spirit of Emil Wetten.

Wetten holds the record for amassing the lowest percentage of the vote of any Republican running for mayor this century. He garnered 15.8 per cent against Edward Kelly in 1935.

But Block feels ambitious. Ever since he saw the movie "Rocky," shortly after being tapped by the GOP, Block has been saying things like, "I'm a contender in the championship, and I want to go the full 15 rounds, Rocky lasted the 15, but lost the decision. But in his heart he won."

Block thinks he can beat Wetten, and is looking beyond the vote total of former Alderman John Hoellen, who ran against Daley in 1975 and staggered away with 20 per cent of the vote. Hoellen is still paying off his $50,000 campaign debt at the rate of $750 a month to a local bank.

But even Rocky would have trouble maintaining his enthusiasm in this race. Bilandic's campaign chest is brimming with about $1 million in donation from labor unions, businessmen and ethnic groups like "Croatians for Michael A. Bilandic" (the acting mayor of Croation ancestry).

Block has less than $100,000, and much of that has come from just two sources. One is insurance tycoon W. Clement Stone, $12,500 (Block also read Stone's book on Positive Mental Attitude after he saw "Rocky" and successfully hit Stone for a donation), and GOP Gov. James Thompson, $22,797.

Because Thompson played an important part in previling on Block to run instead of permitting the GOP nomination to go by default to perennial candidate Lar "America First" Daly, and because Thompson has aspirations for higher office, he can't afford to have his reputation as a vote-getter sullied by a Bilandis rout Tuesday.

But a rout it will be. Not even the Republicans can whip up much support for Block. The GOP county chairman speculated publicly that he isn't sure Block is a genuine Republican, but at least he is preferable to Lar Daly.

And Thompson abandoned Block on a press-the-flesh campaign swing to trot over to City Hall, there to appear with Bilandic in a joint press conference announcing a multimillion-dollar road construction program for Chicago.

Bilandic is not without credentials. Besides the aformentioned road project, which Mayor Daley had failed to clear through the state capital and the federal government, Bilandic also surcceeded in ending the infuriating 25-year-old ban on fresh meat sales after 6 p.m. in Chicago, averted stikes by teachers and lyric opera performers, ended a gravediggers' stike and always manages to appear wherever new construction and community development plans are unveiled.

In moments when Block realizes he isn't Sylvester Stallone, he is philosphically resigned to his fate: "I'm campaigning to win, but I'm realistic enough to know what my changes are."