Trouble is, high season combined with (I presume) airport/tourist area prices. If you want to save loads, look at outlying cities (not just off airport in the same city) accessible by public transport.
Europcar Lisbon locations for your dates - €2000
Europcar Santarém for same dates - €500
(Prices from the Europcar site just now)
Pros - save 3/4 of the total
Cons - 10 mins metro to Oriente, 40 mins train to Santarém, short taxi ride (and ditto in reverse); office closed weekends so you'd have to return it a day early and stay overnight in Santarém or Lisbon on your last night.
This is just an example, I am not pushing Santarém or Europcar! If flying into Faro, fewer options exist of this kind, but would also work for Porto.