Councillors have recommended increasing council tax by 16%, deciding against calling for a 21% rise which would have been the highest ever percentage increase in Wales.
Pembrokeshire council's cabinet met earlier to discuss three options for the increase: 16%, 19% or 21%.
The council faces a projected funding gap of £31.9m, according to the Local Democracy Reporting Service.
A final decision will be made at a full council meeting on 7 March.
Council leaders, whose authorities fund social care, schools and refuse collections, say cuts to grants and agreements on teachers' pay leave them with gaps in their budgets.
Speaking ahead of the debate, Pembrokeshire council's deputy leader, Paul Miller said the fact the county has the lowest council tax in Wales meant it needed a higher rise.
Mr Miller told BBC Radio Wales Breakfast all councils in Wales were facing "extreme financial pressure", but Pembrokeshire had a greater need to increase its council tax revenue.
"It's clear from those numbers that we've got to take pretty decisive and pretty difficult decisions to ensure that we can balance the budget here," he said.
"As the pressures have built, as central government financing has reduced and as inflationary pressures have appeared, our ability to use council tax to meet those pressures is much reduced compared to our peers."
Mr Miller added that even raising council tax by the highest option of 21% "doesn't come close" to bridging the gap and that there would also need to be cuts in services.
"We've only really got two choices: one is to reduce our expenditure and the other is to increase our income through council tax.
"We're attempting to find the right balance between both this morning."
How much will council tax cost in Pembrokeshire?
The average Band D base council tax for Pembrokeshire is currently £1,342.86.
In Ceredigion and Carmarthenshire it is £1,553.60 and £1,490.97 respectively.
Cabinet members in Pembrokeshire are being asked to recommend one of three options for a council tax increase, 16.31%, 18.94% or 20.98%.
These increases would increase the annual council tax bill by £219.02, £254.34, and £281.73 respectively for the average Band D property.
Council leader David Simpson added: "During the past decade, funding levels from UK government to Welsh government and on to councils have not kept pace with the ever-increasing pressures.
"Due to this, we have had to make significant budget savings of £96.7m over this time.
"We have always endeavoured to minimise the impact to service users, especially the most vulnerable in our communities."
A final decision on the council tax level - and any cuts it needs to make - will be made by full council when it sets the annual budget on 7 March.
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