(Edited to add: Rats. I was writing this while Vomaxx posted. Sorry for the partial repetition.)
I don't want to be a downer, but here's the honest answer:
Probably not.
Do *some* people make a living writing novels? Yes. But even many writers whose books are on your shelves right now still have day jobs. It's one of the toughest ways there is to make a full-time living.
If you haven't finished your first novel yet, the "when" could be very far off, if it happens at all. Most people do not sell their first novels. For some, it takes three, four, or more manuscripts before they have written something publishable.
But even if you get that far, an editor will probably offer you less than $10,000 for your first advance. (I think mine was $2500-- and that was a nonfiction book, which is easier to sell.) There is no guarantee that you'll ever see anything beyond the advance money. If you count up all the hours it took you to write, edit, submit, proofread, publicize, etc., there's almost no way that first book can be financially worth it unless you break out right away to bestseller-like numbers (in which case, your royalties may be very good).
Keeping a day job (or having a really understanding spouse with a great job) is imperative until you can actually live off your book money.
It is easier-- though still not "easy" by any means-- to make a living as a nonfiction writer. I've done it for the past 9 years, writing mostly for magazines and books I was hired to write.
With fiction, I believe the question really has to become this:
"If I knew I'd never get paid for my writing, would I do it anyway?"
If so, you have nothing to worry about. Write because you love it, write because it's a challenge and a creative outlet and to share with people you love-- and if the money follows, it's a bonus.
If not, you may be setting yourself up for a world of frustration. There are about 6 bazillion easier ways to make money out there.
My vote? Finish the book. See how you feel about it. See if this is something you want to keep doing, to keep perfecting your craft and learning. See if you're willing to have a day job and write during your "free time" at night or in the early mornings and weekends. If so, be patient with your talent and see where it leads you.
Good luck!