Oak Bluffs selectmen again postponed a decision about their appointment to the Martha’s Vineyard Commission after a lengthy and at times heated discussion Tuesday.

A new slate of commissioners was elected in November and will take office in January; every Island town also appoints a voting member to the regional planning agency.

In Oak Bluffs three people had expressed interest in the appointment: Susan Desmarais and John Breckenridge, who both ran on the November ballot but were not elected, and Abe Seiman, who has served in the past as a member of the MVC. Mr. Breckenridge is currently serving as an appointed member.

The town appointment was on the agenda for the selectmen’s Nov. 29 meeting, but when Ms. Desmarais was the only one to attend, selectmen said they wanted to hear from all three candidates and postponed the matter to this week.

On Tuesday they learned that Mr. Breckenridge was withdrawing his name from consideration because of medical concerns. “I’ve been proud to serve the town for the last 12 years,” he wrote in an email to the board, urging them to appoint a well-rounded candidate.

Ms. Desmarais again attended the meeting. Mr. Seiman did not. Nevertheless, four of the five selectmen appeared reluctant to appoint her this week, lamenting Mr. Breckenridge’s decision to withdraw and suggesting that the town advertise for more candidates..

“I don’t think we all can thank John enough for his service to the commission,” selectman Michael Santoro said. “I know it kills him to step aside . . . He served us well. And we’ve got some big shoes to fill.” He said he would like the position advertised.

Selectman Kathy Burton agreed. “I’m thrilled and encouraged by other people wanting to jump in to service,” she said, but she wondered “who would truly represent my thoughts and feelings, and I know John so well . . .  he truly advocated for me.”

Walter Vail had similar remarks. “I might have felt differently if John had stayed in as a candidate. Now that he’s gone I’d like to see us open it up too,” he said.

Mr. Vail offered words of appreciation for Ms. Desmarais but stopped short of backing her for the appointment. “I think it would be well if we had a chance to spend more time with Susan,” Mr. Vail said. “It’s such an important position, I’d really like to see other Oak Bluffs residents step forward and say ‘I’d like to serve on the commission.’”

Board chairman Gail Barmakian had a different view, noting that in the past selectmen had made appointments without advertising, and that shouldn’t change because Mr. Breckenridge withdrew.

“Let me just say I think it’s unfair at this point.” she said. “We have two candidates, Abe and Susan. Abe is not here. Susan obviously has shown interest and had run and had a good showing in the vote. I think it’s the right thing to do at this time, both to honor the will of the voters as well as this process.”

But selectman Greg Coogan echoed others that the board should advertise.

“The tenor I get from the board is that John was a comfortable member of the commission, and without putting words in everybody’s mouth I think . . . he had a pretty good shot of getting reappointed, is one way of looking at it,” Mr. Coogan said.

Planning board member Ewell Hopkins said Ms. Desmarais was a strong candidate who received a high number of votes in every Island town. And he said Mr. Seiman has experience on the commission.

“I believe you have a very strong supported candidate from a populist perspective and a candidate with a record you can look at,” he said. “I encourage you to look at those two candidates.”

Mr. Coogan said the election results should not matter. “It’s not about votes,” he said. “It’s about who do we feel represents us.”

But planning board chairman Brian Packish said the vote should matter to selectmen. “At the end of the day I voted for you so you would be an extension of me,” he said.

Joyce Dresser criticized the selectmen for handling the matter poorly. “I think this is really an insult to Susan and a slap in the face, that having put herself out there, gotten so many votes, well we don’t think you’re good enough,” she said. “That just doesn’t sit right with me.”

Mr. Santoro said the audience made good points, and said he had been impressed with Ms. Desmarais at their last meeting. “I would love to hear comparisons to other people,” he said.

But Ms. Desmarais told selectmen if they postponed a decision, she didn’t “want anything to do with it.”

“I am really, really frustrated right now,” she said. “What I’m hearing is you’ve never done this in the past and you’re doing to do it now, and the will of the voters is not enough to do this appointment. I feel I’ve shown my commitment, shown my interest.” She said she told each of the selectmen she was available to talk more if they had questions.

“This feels to me like the politics of Tammany Hall and it absolutely is shameful,” she said. “I voted for each of you and I won’t vote for any of you again.”

“I’m sorry you feel that way,” Mr. Santoro said.

Selectmen now will advertise the position.