CARACAS, Venezuela (CNN) -- Venezuelans swarmed the polls on Sunday to cast ballots in hundreds of gubernatorial, mayoral and legislative elections.

President Hugo Chavez has been campaigning hard for what he calls "my candidates."

But for President Hugo Chavez, the election is about himself -- and he's not even on the ballot.

Widely seen as a test of his influence over voters, Sunday's elections are the first since Venezuelans shot down a referendum that would have allowed Chavez to run for his third six-year term.

Turnout was high for the voting, electorial officials told The Associated Press.

Major losses by his ruling PSUV party Sunday would deeply damage any effort to place the referendum on the ballot again.

"In the final tally," political analyst Luis Vicente Leon told CNN in a recent interview, "it's not the election of governors and mayors that he is looking for.

"He is looking to show the country an electoral triumph to wipe a little of the egg off his face from his defeat in the constitutional referendum, starting with the premise that President Chavez desperately needs to have another referendum to have continuous re-election."

A loss for Chavez's party also would weaken him at a time when he has suffered several defections from his Fifth Republic Movement.

Likewise, victories by his party would help cement his grip on power.

Chavez has said in speeches in which he calls opponents "thieves" and "capos" that his 10-year-old government's fate is at stake.

He refers to "my candidates" and talks about the votes being for him.

"If we do everything we have to do and we don't leave one single vote for Chavez out of the ballot box, we could win all the states in Venezuela," he said at a boisterous rally earlier this week.

Winning a majority of the mayor's and governor's races would be the fastest and easiest way for Chavez to continue his socialist revolution, says political analyst Nelson Merentes.

At stake Sunday is 22 governorships, 326 mayor's posts and 233 legislative seats. Six of the governorships are in the hands of the opposition.

Analysts will be paying particular attention to Chavez' home state of Barinas, where his older brother is running for governor.

A loss in that race "could cause President Chavez much symbolic damage because he would be losing in the cradle of his revolution and around his family," said Leon, who is with the Datanalisis polling firm.

Chavez also could run into trouble in three other heavily industrial states, analyst Merentes told CNN.

Although Chavez has said he will honor all election results, he also has made statements that the opposition sees as threatening.

Speaking in Carabobo state, Chavez said, "If you allow the oligarchy to return to governing, maybe I will end up taking my tanks from the armored brigade to defend the revolutionary government."

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CNN's Patricia Janiot and Journalist Maria Carolina Gonzalez contributed to this report.