If you're just thinking about starting your flight training, don't even think about the furloughs at the major/legacy/even regional level right now.
You're years away from having the experience necessary to get hired. Start your training, see if it's something you like, keep going if it is. Build time, wait out this downturn, and by the time the cycle goes back on the upswing (and it always does) you'll be ready to get hired in the next wave.
With everything that has happened in the last few years, and is continuing to happen, the only question you can think to ask is "Should I start training now, or wait?" The question should be: "Should I become a pilot, or should I pick a career that is easier to get into, pays more, and has better job security?"
I started college in 1988 and there was NOTHING going on, furloughs, airlines going belly up, etc. Even 1993 sucked when I graduated. The guys that got out weren't in a position to capitalize on the eventual upswing.
If it's something you really really REALLY want to do, then do it.
If it's something that you think is going to score you chicks, fat pockets and prestige, well, meh.
There is a tremendous amount of negativity in flying. Much of it is justified as the career is very difficult (for many reasons), and even if it wasn't, pilots aren't exactly the group of folks to just see the bright side.
So, in my opinion, the only good reason to pursue a pilot career is if you love flying so much that you doubt you will be happy doing anything else. And the only way to find that out is to fly! Watching Top Gun, or enjoying being a passenger on the airlines and thinking "gosh this would be an awesome job" doesn't really tell you much about yourself, or about flying.
I therefore recommend that you take the advice that has already been mentioned in this thread - get your private (as inexpensively as possible), see how much you enjoy actually flying, and then take it from there. Remember, baby steps!