Can anyone think of a good tactic for knowing if an air drop is coming early on? I emphasize early because at that time frame every resource is even more precious and I need to build my army. I can't just put a strand of marines surrounding the enemy base, the drop could fly out from anywhere and sneak over. I'd like to know before they make it to my base but what's an efficient and cost friendly way of monitoring this?
I think both of the answers here are good answers, but since you seem unsatisfied let me try to contribute.
When playing as Protoss or Terran I often find its useful to use my Pylon/Supply Depot to help give me vision around my base. This isn't, by any means, a replacement for scouting, but it does give me a little advanced notice on drops. Since most maps have your main on a cliff, spreading out these (otherwise useless) structures helps monitor not only the edges but extends the range of your viewing.
Now this technique won't stop a drop, and it won't even really give you too much advance warning, but when every second counts, these are invaluable. You also have the benefit of power for Warpgates. If your opponent drops near the edge, these aren't advanced enough warning, but they do provide a nice distraction while you move your army. If he bypasses them and moves to your mineral line, they're a more advanced warning.
By comparison, Overlords almost trivialize this problem as you can spread them about the map, around your base and even around your opponent's base.
I know its not a solution, but it should help.
The truth is, there is no cheap, effective, sure fire way to guarantee you catch drops. Certainly map control helps, as does scouting, but if there was an easy fix for this terran's would probably never drop.
You have a few options:
I recently had a match where because of my overlord placement and watch towers, I saw his Banshees move out. Gave me plenty of time to get Overseers, Hydras and an extra Queen to defend.
Take a look at Map Control for more info on just that: Map Control which relates to determing what your opponent is doing.
As it sounds like you are playing Terran.
Sensory Towers - I can't recommend them enough, And follow those up with perimeter Turrets starting in the back of your base to nail those incoming drops.
It also doesn't hurt to place a solitary marine at each watchtower.