I'm not going to say that it cannot be done. I went from scoring 590s on practice exams to a 640 to a 690 with a months effort altogether. I was lucky that I had all the free time in the world and a quiet place to study. You can do it, but be prepared to a) be seriously challenged and b) consider the possibility of writing the exam twice.
Here's how I would go about it:
Concentrate on Quant first, sounds like you have lots of room for improvement there. You already have a baseline so go ahead an buy Manhattan's GMAT set then start doing every book piece by piece. GMAT requires you to understand your concepts very well - it's not about how much you know but how well you know it and that's where Manhattan really helped me out. Going through bit by bit and ACTUALLY recognizing what I had learned over the past 24 years of my life was very important (I didn't realize that every number is basically formed by a few building blocks - prime numbers, until I started studying for this exam. Call it a damming review of my education or an oversight on my part, it's still a substantial difference in thinking). After you're done going through these books, you should have a decent base to attempt another round of practice. Here, you should get the GMAT Official Quant Guide, there are tons of relevant questions in there. Start going through them one by one. There are 200 I think. Do the first 100 without a timer and then go back and see where you messed up. Now make an
error log (this website has a few examples) and start writing down the reason. Did you not understand the question, or was it a silly mistake? Also write the topic down. Now have a look and see what stands out. For me, it was overwhelmingly arithmetic mistakes and not reading the question properly. Eliminating these simple mistakes alone was probably worth 20-30 points.
Now, go through the next 100 questions AND TIME YOURSELF. Get into the habit of moving on from questions that you cannot solve - it'll hurt you in the end if you get stuck. Repeat the error logging process above. Now, get some practice CATs (included with Manhattan, some on this website and Kaplan has nice ones too) and solve those. I find the Manhattan ones to be harder than the actual tests so get used to being disappointed. Now review these questions again and see where you made the mistakes. Are there any topics that you STILL do not understand? Go back, review those and try another CAT. This process alone should take you 2 weeks.
Now for the Verbal section. I was fortunate here that I did not have to study too much. I read a lot of books and enjoy writing essays so much of it came together nicely for me. Unfortunately, here, you just have to start getting used to the nuances of the English language and reading more and more is very useful. But since you're pressed for time, that's not an option. Instead, you can rely on the Manhattan set (only 3 books for Verbal) and get a few basic concepts down. I would attack Sentence Correction first since the rules are straightforward to memorize and understand (concentrating on the subject when trying to decide between single vs. plural, using whether vs. if and so on). I would also recommend Aristotle's SC Grail, it's to the point and gives you plenty of pointers. Getting these down will also help you save time for comprehension reading, which is what I would look at next. Here, focusing properly and understanding the passage in one go is extremely useful as you can just go back to the question asked and instantly know which area to look at. Being able to understand the context is extremely important too. Practice makes perfect. Then comes Critical Reasoning, which I think is the hardest part of Verbal. You really have to tune your brain to think in a logical and objective manner and that takes some doing. Follow the examples you get in the books and try to use all the examples you can find. You will eventually catch on. This should ideally take you a week.
So that's 3 weeks gone. Now concentrate on getting as many practice CATs as possible and do them (do one a day) and then keep going back and reviewing your mistakes. Spare a day to review IR and AWA (a polished essay is always great when applying for an elite school). Save the two official tests on GMATPrep for last as they'll give you the most accurate estimate regarding your score (I scored a 710 the night before). Take plenty of breaks when you're studying, don't get distracted and don't overstress yourself. Can't solve anything? Fine, take a 20 minute break and get a snack. Play a game, or watch some TV, whatever it takes to relax your brain.
If you do this regularly, I'm quite sure you'll be able to boost your score by a substantial amount. It's honestly all about the effort and training your brain to think quickly. Put your head down and go for it.