Here's the thing I see. The industry "today" is mad for pilots. The question I would be asking myself if I were in your shoes is this.., If I really want a career in flying, I already have a bachelors, so I've filled the Major airline requirement there. Anything above a Bachelors is overkill (as far as the airline industry is concerned) If I start flying now, In a year (or less) I could be CFIing and perhaps be hirable by the end of '08 or spring of '09. Hiring is "expected" (so I've read) to continue for some time. So I would say, providing there are no unexpected curve balls in your life, you have a better than reasonable chance of at least being picked up by a regional carrier in the next 2 years.
Now, lets say you finish the masters program and then pursue flying anyway. Is the Masters degree a thing that is perishable? In other words if you decide 3 or 5 or 10 yrs from now that flying for a living is not what you thought it would be and you would like to get back into your previous profession, would you be able to do it having not worked in the field and having a X-year old grad degree.
I would say it all comes down to what you truly want to do with your life and what you actually CAN do financially and so on. Me, I would probably get into flying now, there's a very high likely hood things are going to continue to go well from the hiring stand point and the money spent on a degree that may or may not get utilized can be spent on something you will actually use and grow a career with. just my 2 pennies Best of luck!