Around the National Football League, the prevailing sentiment is that the search is on for a successor to Bart Starr, that the one-time idol of Green Bay has failed miserably as coach of the Packers.

That hard-line opinion, often voiced by people who see the Packers play perhaps once or twice a year on television, melts considerably the closer you get to that iceberg on the northeastern corner of Wisconsin.

Certainly there is frustration over the team's fall from the glittering heights of the Lombardi era, when championships became commonplace. But the memory of the quarterback of five title teams, a 17th-round draft choice from Alabama named Bart Starr, still lingers.

The reason is that the Green Bay franchise is unique. It is the only publicly owned team in the NFL. The 4,738 shares of nonprofit stock are owned by 1,761 shareholders, most of them lifetime fans.

Obviously, these are not the fickle fans of other cities. Many are the same loyal supporters who cheered for Starr in the '60s and now, despite advancing age, think nothing of sitting outside for four hours in a roofless stadium rooting for a loser when the wind-chill factor is below zero.

Sellouts are assured whether the team plays in the high-school atmosphere of Lambeau Field or in Milwaukee's County Stadium, and a majority of the customers would fit right in at the daily shuffleboard action in St. Petersburg, Fla.

Dominic Olejniczak, 73 and barely able to walk, has directed the Packers' seven-man executive committee for 24 years and admits he's always been a Bart Starr fan. Many felt as long as he had control, the coach's job was secure.

There has been a change, how-ever, that has increased speculation about Starr's possible departure. Because of Olejniczak's failing health, Robert J. Parins, vice president of the club, was given the authority Oct. 11 to run the organization, and it is widely assumed he will be named president at the annual stockholders' meeting in May.

Parins, 63, a county circuit court judge since 1967, is a community leader. Despite losing his right arm in a bicycle accident when he was 12, he is an avid fisherman and golfer (a 20-handicapper) who also raises horses as a hobby.

"I feel very confident that all members of the executive committee share the same feelings as the fans," he said recently. "We're not happy when we lose, and we want to do everything in our power to help our franchise be successful.

"I'm not going to be drawn into any discussion about the coaching staff," he said when asked about Starr's status. "I don't want to discuss it at this time."

Starr's four-year contract will expire at the end of the season, and many NFL observers say that unless the Packers at least break even at 8-8, Parins will begin his regime with a new coaching staff.

When Olejniczak was incapacitated last December, Parins played a major role in the reassignment of administrative responsibilities, including stripping Starr of his title as general manager. However, the coach still has complete control of all player personnel decisions, such as the recent signing of wide receiver John Jefferson.

Starr says he is weathering the constant criticism, which a few weeks ago included a statement by former teammate Herb Adderley. Speaking at the Pro Football Hall of Fame in Canton, Ohio, the former defensive back said: "If Starr doesn't finish with a .500 record, he's out this season. There is no discipline and there are other serious problems."

After the Packers' dramatic come-from-behind 26-23 victory over the New York Giants Sunday, Starr was asked how he is holding up amid the turmoil and widespread speculation about whether he will be fired.

"Fine," he said, trying to force a smile. "Emotionally, this is the kind of victory we can build on. Once you've experienced something like this (rallying to win in the closing minutes), it helps you.

"Right now I'm very pleased with the way things are going," he continued. "This will keep the second half of the season rolling in the direction we want."

After winning two games in a row for the first time since midway through the 1978 season, the Packers are 4-6. Upcoming are Chicago, Detroit, New Orleans, Tampa Bay, Minnesota and the New York Jets.

"Even a 7-9 season might save Starr's job," said a source close to the team. "After winning only five games the last two years, 7-9 after losing six of the first eight would look pretty good."

The beleaguered coach has tried to use his popularity as a player to tide him over the difficult years following an 8-7-1 record in '78. He has appealed to the fans' loyalty and recently asked publicly for their support following a poll in the Racine (Wis.) Journal-Times, in which readers voted, 160-19, for his ouster.

"The good, solid Green Bay Packer fan wants his team to succeed and will do all he can to ensure that," Starr said. "Forget the circumstances, situations, personalities. Let's put all those kinds of things aside. The team needs the support of the fans."

One fan, in particular, took Starr's plea to heart.

Ed Thompson, a Green Bay businessman, planned a "Green Bay Packer Support Sunday" when Seattle visited Nov. 1. He helped organize bands in the parking lot and college cheerleaders at each corner of the field, and orchestrated cheers. After the team rallied to defeat the Seahawks, 34-24, he helped organize the same activities in Milwaukee Sunday.

Others, obviously, have given up. Although there was little booing in Milwaukee, the only banner hanging from the upper deck read: "It's Time to Part with Bart."

The final decision apparently will be made by Parins and he, like other loyal Packer fans, is awaiting the results of the final six games.