It is possible to learn any language without any tutor whatsoever. I've been learning several languages all by myself, including english, and I haven't have the need of a tutor.
Of course, teaching yourself is not something easy, you need to be constant and organised, otherwise it will be more difficult to you. You also need a good book of grammar and a bilingual dictionary. Spanish is quite popular, so I think you will not have any problem to find those books. You can go to amazon.com to shop on line. It's a great page, and quite safe.
I'd advise you against learning spanish from the net. I mean, you can use the forums, web pages etc. to complement what you learn from a grammar book, but do not use the net as your primary source of learning. I did it when I was learning korean, and it was really difficult.
The links Paco gave to you are quite useful, so give them a try.