"Always, yes I do [think we have a shot]," he said. "And this is not just trying to sound positive. We've had miracles in the past and this would be a big miracle to make it - maybe even the biggest achievement ever. But it's still possible so why not try?"
Vucinic, who succeeded Tab Baldwin as coach in 2006, conceded his squad is probably the weakest he has been a part of in his 10 years on the Tall Blacks' staff, severely hampered by the double blow of injuries to their two best players.
"We've probably lost 30-35 points a game with Kirk and Tom so scoring will be an issue," he said. "But maybe they'll prove to be a strong team. That's our plan.
"There are always tours where somebody comes out of the blue and plays really well - that's what we're looking for again."
The New Zealand squad features a mix of the young and untested, and Vucinic said they would rely heavily on the few players who have previously had a taste of international basketball.
One of those players in naturalised American Casey Frank, who called the team "in flux" but more than capable of shocking the basketball world.
"I don't think we'd be going if we didn't think we had a chance," Frank said. "By no means is it going to be easy - it's going to be very difficult.
"But that's always been the beauty of the Tall Blacks - the whole is greater than the sum of the parts.
We come together and we play above ourselves and that's always been the way. We're just going to have to do it again."
That's perhaps one aspect Tall Blacks fans can find solace in - the team is rather accustomed to upsetting the odds.
"We've never been the favourite," Frank said. "I don't think I've ever gone into a game where people were telling us we were going to get the win easily. The underdog mentality, that cape suits us perfectly - we wear that with pride and we go into every game knowing that we have to overcome something."
First up for the world No 18 Tall Blacks is the rapidly-improving Macedonia (33) on Monday night, before an encounter with African champions Angola the following day.
"Macedonia just beat Lithuania again without their starters, so they're a strong team and they're going to be a tough proposition," Vucinic said. "And Angola has been at every Olympics for 20 years so they'll certainly want to do that again."
New Zealand will need to win at least one of those games to make the quarter-finals.