We rented while still tourists, no DNI, but did have a garantia (friends, not family). Before having the garantia we did find a landlord willing to rent to us if we paid well in advance. Not sure your financial situation but you could offer 6 or 12 months rent up front, although you'll likely lose $ this way with a declining peso. As for the cost of furnishing, don't forget unfurnished is seriously unfurnished here, at least our house - like holes in the ceiling with wires for light bulbs - no fixtures. It's a large cost but was definitely worth it for us, even for a stay of just 2 years.