Nottinghamshire County Council says it will do "all it can" to avoid closing community facilities because of funding cuts.
On 20 October, the government is due to announce which departments will need to reduce their spending, and by how much.
The county's libraries and recycling centres are among the amenities facing cutbacks but councillors say they are looking at alternatives to closure.
One option being considered is shutting nearby facilities on different days.
In terms of the county's 61 libraries, the authority said it would look at "when we open them and how they are run".
Tim Malynn, corporate director for communities, said: "There's a huge opportunity for the community to get involved in helping in some of the smaller libraries.
"But for many of the libraries we're going to be looking at closing them on different days of the week, maybe at the end of the day adjusting the opening days to suit demands, which is critical.
"In the north of the county for instance, we've got some that are open on Sundays and at one recently-opened library we found over 1,000 people going through on a Sunday, which is incredible.
"For household waste recycling centres, we recognise the fact that people use them.
"They are expensive to run, so in days of low usage we'll be looking at what can be done by way of reducing the number of opening hours and the days they're open.
"But the councillors are also extremely clear that they want to make sure we manage those closures so that people have got an alternative on any one day.
"So if there are two adjacent sites one will be closed on one day and the other will be open."
Mr Malynn said councillors were finding the measures "extremely difficult to reconcile", because they will inevitably lead to reductions in services and job cuts.
In addition, the council is reviewing provision of bus routes, with some under-used services likely to be shut down.
Trading standards, country parks and highways maintenance will also be affected.
The authority plans to save £150m over the next three years to help meet the expected funding cuts, as well as extra commitments to the care of children and the elderly.