"I think the Chatham Cup is something to get us dreaming," Barter said.
"For us, it gets us excited because we know how far we can go ... everything I have seen so far this season tells me we can go on and win this game."
United have not progressed past the first round in the club's six-year history, according to Barter.
"We are really hoping the city can get behind us and have a crowd down there. It is the biggest game the club has had in a long time."
Barter said South Auckland were playing in a league equivalent to the Waibop Federation One competition. He said it would be a tough game but a winnable game, and they had shown this year they can beat teams from higher leagues.
United defeated Matamata 4-1 recently in the Chatham Cup qualifying round.
"For us to have won already, and to have a home draw, we are absolutely delighted," he said. "Being at home we have given ourselves a good chance."
Ngongotaha coach Shane Davis said the competition brings back a lot of history, including a quarter-final run Ngongotaha made in the early 1990s.
He said his team were playing well this season in the Waibop Federation One competition and had a good draw to be facing Pukekohe.
"It brings back a lot of memories. Whenever we play at home [in the Chatham Cup] a lot of old players from Rotorua City and Ngongotaha come out and watch the game," he said.
"There is a great history behind it. When I was playing for Ngongotaha we made it to the quarter-finals and played Mount Maunganui."
Davis said their goal was simply to go as far as they could in the cup.
"That's our aim - to try and go as far as we can," he said.
"We have actually done alright in the Chatham Cup in recent years, we played Melville last year and lost 2-1."
Melville United went on to make the semifinals last year.
Only one Rotorua team has made it to the final of the Chatham Cup. Rotorua City went the distance in 1989 and lost to Christchurch United 7-1 in the final.
Chatham Cup fixtures tomorrow:
*Rotorua United v South Auckland Rangers, Neil Hunt Park (Rotorua) 2pm
*Pukekohe v Ngongotaha, Bledisloe Park (Pukekohe) 2pm