Unless you're exceedingly talented, I fear that full fluency in three years will be very difficult, especially if you're studying at university in the US or Europe.
Based on how students in our U.S. programs perform, I'd say that the best one could hope to achieve in three years would be:
1. Reading. The ability to read a (simple) modern text slowly and with a dictionary.
2. Writing. The ability to write about very simple topics, with a minimun of error.
2. Speaking. Able to express yourself on simple topics and understand MSA conversations on the same topics. Probably, one would not be able to follow well, if at all, a conversation in colloquial. (No more than a speaker of Latin could follow a conversation in Italian.)
By the end of the third year, however, you'll be at a point where your level of knowledge will be just about ready to grow at a much faster rate.
All this assumes you're not going to immersed in Arabic for your three years of study. Normally, students get around three or four hours of practice per week, at best. If you can find a way to do two summers abroad and/or a semester, this will help immensely. If you are primarily interested in speaking, this is especially important.
Full immersion is by far the best -- in a place where you'll not be able to speak English. A backpack and a couple thousand dollars will keep you going for a long time in places like Egypt, Jordan, and Syria. If you're willing to forego a few comforts, two or three thousand dollars can easily last a year. I'll bet that's cheaper than your tuition!
As for total words to memorize, I'd humbly suggest that this is the wrong approach. All studies show that this is just about the worst way to learn vocab. Get your first 1,500 words, and then read, read, read. If you still wish to memorize, you'll do better to memorize Qur'an, hadith, proverbs, poems, etc.
I think Sr. Whitelily is correct. Seven years is reasonable, assuming you can spend a couple of those years in an Arabic-speaking country. But even then, you'll probably still have trouble with more complex modern and ancient texts and be able to work in only one or two closely related dialects.