In the steamy Jaycees meeting hall in this city of baths, Democratic candidates for governor have been given four minutes to make their peace with voters, but what Bill Clinton has to say takes only a few seconds.

"I am offering my experience as governor and my experience in losing in 1980," says the one-time wunderkind of Arkansas politics. "I'm asking for a second chance."

Despite rhetoric and imagery about the death penalty, utility rates, teacher salaries and the crumbling economy, Clinton and most everyone else here knows there is but one issue in Tuesday's primary: will the voters forgive Clinton his sins and start him on the road back to the governor's mansion?

Clinton, 35, was the youngest governor in the United States when elected in 1978. A handsome Ivy League lawyer and Rhodes scholar, he was later elected chairman of the Democratic Governors Association. Two years ago, he was a rising Democratic star whose opinions were sought by national columnists and who told the Democratic National Convention how to put the party back together.

But back home, his political mistakes mounted. As he attracted national attention, resentment over higher automobile license fees, an influx of Cuban refugees and an arrogance of style kept building. In the 1980 November election, Clinton ran behind Jimmy Carter and lost to conservative businessman Frank White in a stunning upset.

"I made a young man's mistake," Clinton says. "I tried to do too much too soon. I spent too much time doing what I wanted to do rather than what people wanted me to do. What they really wanted me to do was be more accessible."

Others are even harsher in judgment of his conduct in office, and wonder whether Clinton is truly reformed. But in the 18 months since his defeat, Clinton has worked to persuade people he is a changed man, and the differences are noticeable.

He began his bid for reelection with a round of television ads in which he apologized for his mistakes and promised to learn from his defeat. Throughout the campaign he has told audiences contritely he now knows a politician has to listen before he can lead.

Other small changes are evident. Clinton's hair is shorter and his wife has agreed to be called "Mrs. Clinton" during the campaign, rather than her maiden name as she has preferred. Some of Clinton's staff members, who earned a reputation as a palace guard, are gone.

With a superior organization and a big edge in fund-raising, he is favored to win the Democratic nomination, but there is enough uncertainty to make many nervous about Tuesday's voting.

Clinton has four opponents, including another glamorous young Arkansas Democrat, former representative Jim Guy Tucker, 38, who has been out of politics since losing the Senate primary in 1978. The contest between the two is a political version of the battle of the network stars.

Other candidates include former lieutenant governor Joe Purcell, a quiet campaigner who seems to be the beneficiary of the fallout from the star wars between Clinton and Tucker.

Published polls show Clinton leading Tucker by a wide margin. But the polls are not considered reliable--polls in October, 1980, showed Clinton with a big lead over the Republican, White--and the question is whether Clinton can avoid a potentially dangerous runoff, where Arkansas voters sometimes turn against front-runners.

Tucker, with his political future at stake, has given no quarter to old ally Clinton, arguing that Clinton is the riskiest candidate the Democrats could nominate to run against White in November.

"Why does the only Democratic governor in Arkansas history to lose to a Republican deserve a second chance?" he asks.

The competitiveness between the two is so intense that the campaign has taken a bizarre and bitter tone. "The issue is which one is the more reborn conservative," said Delia Combs, executive director of the Arkansas Republican Party. "I don't think anybody's particularly buying it."

Tucker attacked Clinton for commuting the sentences of 37 convicted first-degree murderers while governor, including 18 after his defeat. One of the men committed another murder after he was paroled.

Tucker's TV ads show him with a shotgun slung over his shoulder, or standing in a feed store talking about harsher treatment of criminals, or on a pistol range as a reminder that he was once a prosecutor.

Clinton, stung by the commutation issue, has fired back just as hard at Tucker, charging that he missed crucial votes in Congress (Tucker says the votes were taken while he was running for the Senate), that he failed to support a workfare program for welfare recipients (which Tucker voted for) and that he received high legal fees from a company that went bankrupt.

Clinton's attacks apparently have hurt Tucker, who last week halted criticism of Clinton, and there is a feeling now that Purcell could slip ahead of Tucker Tuesday and edge into the June 8 runoff, assuming Clinton falls short of the necessary 50 percent of the vote.

But the issue is still Clinton's past performance, and no one knows how much resentment lingers in the minds of Arkansas voters. Clinton supporters believe he will at least win the primary, if only because voters want a rematch of the 1980 race.

Says W.R. (Witt) Stephens, an aging kingmaker of Arkansas politics and a loyal Clinton backer: "It's like your father taking you to the woodshed to punish you. He didn't take you twice for the same thing."