Eighty percent of people who responded to Nottinghamshire County Council's budget consultation have rejected a 5% increase in council tax.
The Labour-led authority asked people what they were willing to pay in respect of a planned increase in council tax.
Of the 6,000 respondents, 45% opted for the smallest proposed rise of 1.99 percent.
A referendum would be needed for a rise above 2%.
Leader Alan Rhodes said: "We've ended up with a £154m budget deficit, so the prospect of a further freeze was not realistic.
"It would have been irresponsible, I believe, in the light of what we inherited."
He added: "However, we did feel it important to ask people what they felt was a reasonable amount."
The Conservative opposition said increasing council tax would hit Nottinghamshire's poorest the hardest.
Councillor Kay Cutts said Labour knew they would have to find savings if they took control.
They had made extravagant spending plans they could not afford and it was now the public who would pay the price, she added.
Nottinghamshire County Council is also consulting on proposals for which services face being reduced/changed as part of its plans to reduce spending.
The consultation ends on Friday.