"We don't always agree, and it's OK if we don't as long as we disagree in the room and leave united," said Goodwin, who was the only candidate nominated for the post.
Encouraging unity seemed to be the theme of the meeting at the Evans Government Center.
"I hope this history in the party, it's got to end," said 10th District Republican Party Chairman Dave Barbee, who presided over a portion of the meeting. "This is important. Unity is important."
In December, the party tried to oust then-Chairman Lawrence Hammond. He disputed his removal, contending that party leaders had not provided him with adequate notice of the meeting.
In March, the 10th District Republican Committee sided with Hammond, saying he received just five days' notice of the meeting when 30 days are required.
Soon after the reinstatement, though, Hammond announced in a letter that he intended to resign.
"It takes a high level of tolerance to work through these types of situations, and I no longer have a desire to commit my limited time to that task," Hammond wrote.
Also in the resignation letter, Hammond noted that he could not protect the "party's image and reputation" from "the behavior of several members of our leadership."
Another resignation came this month from Sarah Harper Scott, the fundraising chairwoman for the county Republicans.
In a letter Scott sent to The Columbia County News Times , she wrote that party leaders were more concerned with maintaining their power than they were with continuing the party's mission of supporting area Republican candidates.
Though many consider Columbia County a Republican stronghold in Georgia, Scott believes that some candidates for state offices have avoided local party functions "due to the internal strife."
Of the 21 counties in Georgia's 10th District, Columbia County's Republican Party is the largest and is a needed "cog" in the "Republican machine," Barbee said.
"The enemy is the Democrats," he said. "We've got a lot of battles. We can't fight amongst ourselves."