Tunnels under Waitemata Harbour are the strong preference of Auckland members of the Automobile Association.
Of more than 6000 respondents to an online survey, 56.4 per cent favoured tunnels compared with 31 per cent wanting a new bridge.
Only 3.2 per cent were against any form of new crossing, and 93.1 per cent wanted the existing 52-year-old bridge kept in place.
Survey questions did not mention a Transport Agency estimate that a pair of motorway tunnels was likely to cost $1.4 billion more - at $5.3 billion - than a new bridge. But 83.2 per cent of the 6030 people who responded believed cost was an important consideration in deciding what to build.
Only 47.5 per cent said they would be prepared to pay a $4 toll to use a new crossing, plummeting to 8.2 per cent when asked if they would tolerate $6.
Only 22.7 per cent would be prepared to pay a toll to cross the existing bridge.
The AA conducted the survey, with its 1.3 per cent margin of error, in preparing a submission on the Auckland Council's draft spatial plan.
AA spokesman Simon Lambourne said the AA believed the plan lacked essential information about many transport proposals. But it believed building another harbour crossing was of considerable national and local importance and wanted it built faster than proposed.
Transport Minister Steven Joyce said in March there would be a strategic need for a new crossing within 20 years, before the clip-ons on the existing bridge needed replacing, although an $83 million strengthening project had eased concern about that.
He acknowledged yesterday traffic on the bridge had flattened recently and the completion of the alternative western ring route by 2016 may "take a bit off the top of it".
Clearance of the motorway bottleneck over the Victoria Park viaduct, once a northbound tunnel doubled capacity next year, may also ease pressure.
"A lot of people blame the harbour bridge for what is effectively a Vic Park viaduct problem, so you may find that the debate drops off a bit once that is finished," Mr Joyce said.
The AA survey also found strong support for three big rail projects promoted by Auckland Mayor Len Brown, although only 15.2 per cent said they would catch trains for primary transport if they could no longer use cars.
That compared with 65.3 per cent who would use buses, 5.4 per cent who would cycle, 5.1 per cent who would walk and 0.6 per cent who would use trams - even though these stopped running on Auckland streets more than 50 years ago.
The most favoured rail project was links to the airport, supported by 82.5 per cent and considered the most important by 43.3 per cent.
Second place went to the $2 billion-plus central city rail tunnel, with 76.7 per cent support and 38.6 per cent giving it highest priority.
Rail across the harbour won 71.3 per cent support, and 21.4 per cent considered it the most important project.
Auckland's motorways were ranked good or excellent by 61.9 per cent, compared with 23.1 per cent for trains and 29.7 per cent for buses.
Train services were rated "terrible" by 14.4 per cent, as were buses by 11.2 per cent and cycleways by 10.8 per cent.