Intuit will always look to our contract staff when we have additional openings...while I have not been with Intuit that long I have seen a number of people move to a perm role and I recommend this as an option to people if I don't have a full time opening at the time. It is a great way to start your career with Intuit.
That being said, you have an offer in hand and you need to carefully evaluate the pros and cons of accepting that offer since their is no guarantee that you will go perm. Is the offer a company you can see yourself having a long term future with? How does it compare to the position with Intuit you are trying to move into? Have you discussed the other offer with your Intuit leaders to see if and when they think they could move you into a perm role?
I wish you the best as you work through these questions...it is a difficult decision that you will be making. Let me know what you decide and thank you for interest.