Winchester hospital bosses say they have been overwhelmed by public support for their bid for foundation status.
More than 10,500 people pledging support have backed the move to give greater freedom to the trust, which runs the Royal Hampshire County Hospital in Winchester.
But union officials say the poor response from staff shows the trust has work to do in persuading health workers that it is a good move.
Doug Smith of Unison said that only 550 members of staff out of more than 3,000 had given support.
Mr Smith said: "There is a great deal of concern as to what foundation status will mean. I have seen people throwing the application forms in the bin.
"More needs to be done to allay fears. There has been little detail given to staff and that generates suspicion straightaway."
Some 140,000 letters were sent to people in the mid-Hampshire area, asking for backing for the move.
It would free the Winchester and Eastleigh Healthcare NHS Trust from centralised control, and hasten the completion of the £20m development at the Royal Hampshire County Hospital.
The trust currently only has the funding to finish the £6m treatment centre on the top floor of the four-storey development.
Under severe financial pressures, and without foundation status, the new block could be empty for years.
Chief executive Rod Halls said: "I'm delighted that so many people have taken the time and trouble to respond and say they will support us.
"What has been particularly pleasing is the fact that so many completed application forms have been returned, with letters of praise for our staff and our services."
Chairman Barbara North added: "It's very heartening to have such a good response, especially when we hear so much about apathy."
Hospital chiefs also want to utilise the greater financial freedom to develop new outpatient services at the Royal Hampshire County Hospital and the Andover War Memorial Hospital faster than they could at present.
They want to use resources more creatively to ease the parking problem at the RHCH and reinvest money from sales of surplus assets into local services.
There is also a member council for people who want to represent their communities and have a greater say in key decisions.
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