Pit,
Put your drill in the adjacent staion to the broach. Then drill the hole to depth, then broach around .003-.005" deep, re-drill so the body diameter of the drill goes .005" deeper than the broach, then broach again .003-.005" deep, then redrill, etc. Broach without coolant. As coolant doesn't compress very well, and it takes up room which would be otherwise occupied by the chip.
While this is a PITA, I've found it will give you much better broach life. The pressure really increases dramatically on the broach the deeper it has to go. By clearing the chip out with the drill every three to five thou, it takes the pressure off.
If you think about how the chip is formed, it comes into the center of the broach from all sides, so the chip mashes into itself, then gets forced down the hole ahead of the broach. So with such a small tool it doesn't take much to chip the cutting edge.
Also I've found that Blaser Vascomill cutting oil (vegetable based) helps out quite a bit with finish and tool life when machining small Ti parts.
If it's a full form broach, it needs to have a vent hole through it too. You can buy a broach like that from Rayco Tool in Warsaw, IN.
http://www.raycotools.com/
You also need to be lined up perfectly which will be difficult given that you can only adjust your location in "X" and there is no provision for adjusting "Y". But I wouldn't even bother getting started if the broach isn't within .0001" TIR to the main spindle.
Good luck.