It depends on how much the law firm wants you. In today's climate, it is kind of hard to get a job working in big law. However, if you do go to one of the top schools (Northwestern, NYU, U Virginia, Duke, Gerogetown, etc...) you will have a better chance at getting a job working in Big law.
You want to do, MBA, M.S. in engineering, and J.D.? Or engineering over MBA? It might take you a few more years to obtain all three degrees, possibly 4 full years, but it is possible. What type of area in law are you going for? Patent law, criminal, international? If it is patent law then you would need to pass the IP law exam and commit your legal studies in that area after you completed the core basis. Your engineering degree would go well with it though.
Getting the Juris Doctorate alone is about 3 years. I have a friend who obtained his in 2 years, but 3 years is the usual time frame, 4 years for part-time students.
Work for the army corp of engineers.
He is about the money, hence his first post. In any case, you should probably do a fellowship after you pass the bar and the IP exam, it will only increase chances of getting a great job.