Council tax would be frozen for a third consecutive year but up to 200 jobs could be lost under a budget being considered by Norfolk County Council.
The Conservative-run authority is looking to make cuts of £51.5m as part of its proposed budget for 2013-14.
Unison and Norfolk Coalition Against The Cuts said such the savings would affect the most vulnerable people.
But the council said it was targeting help where it was most needed and supporting jobs and the economy.
The council's cabinet will meet on Monday to consider the proposed budget.
If agreed by cabinet, and approved by full council next month, about £1.5bn would be spent by the authority during the next financial year.
The figure includes £302.6m raised through council tax, which would not increase.
The proposed savings of £51.5m include cuts of £6m from a housing support scheme for vulnerable people.
Bill Borrett, acting leader of Norfolk County Council, said: "These budget proposals reflect the difficult times we live in, not only for councils and the national economy, but for local businesses and our residents.
"The budget sets out to support Norfolk's most vulnerable people, especially our older people and children, while giving a high priority to supporting jobs and the economy through targeted spending designed to help support local businesses."
He added that "decisive action and sound financial management" over the last two years had allowed the council to propose an additional £8m to support vital services.
"At the same time, we are proposing a Council Tax freeze for a third year running. This is not the time to ask hard-pressed families and people on fixed incomes to pay even more," said Mr Borrett.
'Attack on vulnerable'
On BBC Radio Norfolk, Mr Borrett admitted job losses were inevitable.
"The county council is an enormous organisation. It employs over 25,000 people and each particular department is looking at delivering the largest amount of efficiencies it can," he said.
"I think we will probably lose up to 200 jobs but one has to be realistic. You can't deliver the sort of savings that we need to without that happening."
Jonathan Dunning, Unison branch secretary at the council, said: "The papers that have been released today talk about various restructurings and management reviews, but also in particular areas where we have concerns, such as adult social care.
"They talk about redesigning day services provision and that's one of the areas that we do have major concerns over."
Mark Hughes, Coalition Against The Cuts: "Whilst the savings are at county level, they have come from cuts from central government.
"It's another attack on vulnerable people. People who need local services the most are going to have to suffer once again because of the cuts that are imposed by the Conservative county council"