Conservation Minister Nick Smith is considering whether to grant concessions for the developments, which would be built on prized parts of the conservation estate. The minister told the Herald the poll reflected the polarised views on the proposals.
"People recognise the huge importance of New Zealand's visitor industry, but equally are quite cautious about New Zealand's most precious places, of which Milford has got to be at the top of the list."
Dr Smith, who is one of the greenest National MPs, said the decision whether to grant access to the national parks was a tough one.
"You don't get much more spectacular than the Routeburn and Milford Tracks, both of which I've done. It's a very difficult call in that I take the view that national parks are areas where nature rules and human needs come second."
Labour Party conservation spokeswoman Ruth Dyson was surprised by the level of support for the developments.
She said in her consultation with New Zealanders the monorail project was more popular than the tunnel because it was considered less intrusive, and the fact the poll asked about both projects together may have led to the higher-than-expected support.
The $170 million Dart Tunnel would cut through the Mt Aspiring National Park and a World Heritage Site, with one of its entry points visible from the Routeburn track. Either of the two projects would halve the one-way travel time of 4 hours. Labour and Greens opposed both projects.
Green Party conservation spokeswoman Eugenie Sage said it was senseless to propose such intrusive projects in areas which were so central to New Zealand's tourism brand.
The applicants for the projects expected the improved access to draw an estimated 20,000 visitors a year to New Zealand, in particular tourists who would not sit on a bus for a nine-hour day-trip.
Dr Smith's decision related only to the access to conservation land, and not to the potential effect on Te Anau's economy. If approved, the two projects would still have to gain resource consent.
Some opponents said that the minister's approval would encourage the local councils to "rubber-stamp" consents for the developments.
A parliamentary select committee will this week consider a petition by the Stop the Tunnel lobby group, which has collected more than 25,000 signatures.