Foreign policy was a signature issue of her late brother, Lindsey Graham.
The DOJ could still appeal within 60 days of the decision but plans are unclear.
Commissioners are expected to review the budget, as the county is projected to face a $178 million shortfall.
If voters pass the propositions, they will see a 9-cent property tax increase.
While most county business can be conducted with three commissioners present, the county's budget needs one more to pass. If the boycotting commissioners don't show, it could lead to budget cuts.