Ola from Portugal,
My husband and I have lived in the Algarve for many years and also pay €1200 per month for rent. We spent between €2500 to €3500 per month for our total expenses. $2000 or less would be doable, depending on your lifestyle. Keep in mind the dollar to euro ratio that changes and you will need to carry private health insurance since Medicare does not work here. There will also be costs associated with getting settled like opening a funded bank account and more. A great source of info is a Facebook group called Americans & Friends PT that has plenty of PDF documents with all things pertaining to Portugal.
Hope this helps.
Terry Coles
Portugal Contributor