Welsh Local Government Association's budget warning
Health spending is expected to get a boost when the Welsh government unveils its draft budget for 2015-16, cut from this year's £15.3bn to £15.1bn.
Ministers have already warned local councils they face cuts of up to 4.5%.
The Welsh Conservatives claim Labour has failed to protect the NHS, while Plaid Cymru says other areas are being cut to "bail out" health boards.
BBC Wales understands Labour has discussed the budget with the Liberal Democrats ahead of Tuesday's unveiling.
Steve Thomas, chief executive of the Welsh Local Government Council said councils were facing the prospect of more budget cuts, which would effect staff and services.
He told BBC Wales economics correspondent Sarah Dickins it was calling into question whether councils could actually deliver in areas such as environmental health, which were facing year-on-year savings.
30 Sep 2014