Barbour was sworn in on Tuesday at the state Capitol in front of a crowd of thousands that included Mississippians from all walks of life, former governors, lawmakers and other elected officials.
Barbour said during his campaign voters told him job creation was the greatest need in Mississippi.
"I listened very carefully. I appreciated the fact that he didn't list 19 things," said McCoy. "He listed what is truly the priority in this state and that is attain and retain quality jobs, gainful employment for our citizens."
McCoy said that Barbour had reached out to the Legislature and lawmakers had reciprocated.
Barbour also addressed the need to continue to improve Mississippi's schools.
"The only thing we have to go on is his word. He said he would. I know that's what the number one concern of the general public is -- good schools," said Frank Yates, executive director of the Mississippi Association of Educators (search), the state's largest teacher union.
"Naturally, we have concerns about funding for schools and other issues. So we look forward to a good working relationship," Yates said.
MAE had endorsed Democrat Gov. Ronnie Musgrove (search), who lost to Barbour in the November election.
Rep. George Flaggs, D-Vicksburg, said he appreciated Barbour's emphasis on unity and said he's giving the Republican the benefit of the doubt.
"I echo his fiscal concern about government. I think that government ought to be simple and without waste," Flaggs said.
Rickey Cole, executive director of the Mississippi Democratic Party, skipped the inauguration celebrations at the Capitol.
"I'd rather go to a rooster fight," Cole said.
Cole said he isn't convinced Barbour will be as cooperative with lawmakers as he's promised.
"Talk is cheap," Cole said. "I think it's really too early to tell. We'll have to see what legislative initiatives he gets behind, the direction he wants to take state policy."
Former Gov. Kirk Fordice, the first Republican elected governor since Reconstruction (search), said Barbour is wasting his time by trying to work with the Legislature.
"The thing to do is get your agenda done," said Fordice, who served two terms from 1996-2000. "And you've got to push it because they'll be fighting you every step of the way."