Hampshire County Council faces a budget shortfall of £140 million due in part to the government’s ongoing austerity programme.
The authority has launched a survey to ask residents about "potential" council tax increases.
By 2019/20, the authority is expecting to face a gap of £140 million as a result of austerity, demographic changes reflecting increases in demand for some services and inflationary pressures.
Hampshire County Council leader, Councillor Roy Perry, said: “Although we have been preparing for this challenge for some time, finding these additional savings is inevitably going to be extremely tough.
“This is because we have already made significant reductions in our spending over the last nine years to the sum of £340 million.
“The picture is worsened by the fact that central government revenue support grant funding for Hampshire will cease altogether in 2019/20 – but demand for county council services continues to rise.
“The steps that we have taken so far, which have served us well, have included securing savings early, reinvesting in new, more efficient ways of working, and making prudent use of our reserves to meet gaps in funding.
“However, we now have to consider more radical ways of making ends meet, at the same time as protecting vital public services.
“The Serving Hampshire – Balancing the Budget consultation asks residents and stakeholders to give us their views on a number of high-level, strategic options including potential changes to services, further ways to generate income, use of reserves, potential increases to council tax and changing local government in Hampshire.
“It is important to stress that at this stage, the county council is not proposing specific changes to services. Any proposals will be informed by feedback from this consultation and subject to further, more detailed public engagement. Therefore, only examples of possible service changes have been provided.”
The consultation is open until 11.59pm on August 21.
Feedback will be used to inform final savings proposals put to select committees and executive members, before consideration by the full county council in October this year.
The survey can be completed online.
Paper copies may be requested by emailing firstname.lastname@example.org and they are also available from Hampshire libraries.