New Zealand has strengthened its relationships in Africa and in the Caribbean, establishing a diplomatic post in Addis Ababa, Ethiopia, where the Organisation of African Unity is based, and in Barbados.
Mr McCully is in New York with Permanent Representative Jim McLay for the final days of campaigning and the vote which is expected to take place about 3am tomorrow.
New Zealand, Turkey and Spain are competing for two seats for 2015 and 2016 in the grouping known as Western European and Others Group.
The winners will be the first two countries to get two-thirds of the votes.
It has been a 10-year campaign, launched by former Prime Minister Helen Clark in 2004. Mr McCully has campaigned extensively for six years at meetings and receptions in the world's capitals, in multilateral and regional forums, and at the United Nations itself.
"If you don't go to any of the events, if you don't go to any of the receptions and you don't do the international travel, people just don't think you care that much."
Mr McCully has used special envoys, including former Prime Minister Jim Bolger, former Commonwealth Secretary General Sir Don McKinnon, and former UN diplomat Colin Keating to help in the campaign, as well as Labour's shadow foreign minister David Shearer.
Mr Shearer said yesterday he was "excited and optimistic" about New Zealand's chances.
"I'm getting to the point where I would feel pretty disappointed if we didn't get on to it."
He believed Turkey was the strongest second contender because the Middle East was hugely important at the moment and having Turkey on the council would be seen as a good thing.
It had also spent an "enormous amount of money" in small countries in a bid to win them over.