The America's Cup match is due to start on March 6.
Hutchinson says they will need their personnel in Auckland soon, with their first boat to arrive on June 20.
American Magic would pay for the mandatory quarantine on arrival for their more than 60 foreign nationals, and any related costs, but according to Hutchinson, they would need to be given the green light by mid-June to get their people into the country.
The alternative is to delay the Cup or move it offshore.
"It's hard to even entertain the idea of going elsewhere or of postponing the event. I've had really candid communications with Grant Dalton [Team New Zealand chief executive].
"We have a very good relationship and he understands our position and the team's position.
"He also knows we do need some action."
Hutchinson's remarks have been echoed by INEOS Team UK chief executive Grant Simmer.
Speaking to veteran Australian yachting commentator Peter Shipway on his Cruising Yacht Club of Australia podcast, Simmer said he was frustrated by the lack of communication from the Government.
"They haven't told us when they are going to give us work visas and so we don't know when we can come down to New Zealand. We need to get a forward party there to set up the base and start things happening," Simmer said. "The New Zealand Government have been silent on that."
Asked earlier this month by the Herald about allowing non-New Zealand crew members to enter the country, Sport and Recreation Minister Grant Robertson was non-committal, but was hopeful the Cup will proceed as scheduled.
"It's early days and I don't have a definitive answer on that," Robertson said.
"I absolutely get the ambition, and know they'll be champing at the bit to get here.
"Getting into next year we're all going to be wanting things to look forward to; to bring the country together, to get the economy pumping."