For drilling holes under 1/2" in any annealed tool steel set your drill on the slowest speed, (unless you have a very high quality press that is both extremely slow and rigid) make sure your bit is sharp and use a good cutting oil. WD is way to thin. I love MolyD, it is messy but very good. If you use a pilot hole on the larger holes the pilot bit should be very close to the size of the distance between the 2 flutes at the tip of the large drill. Use quite a bit of pressure until you feel the tip go thru then back off. A good drill in a solid press, at the correct speed and pressure can cut and spiral out the material in a couple long ribbons.
To high of speed and to little pressure will cause the tip of the drill to rub more than cut. The heat on the cutting edges of the drill will become extremely hot very quick. This causes the bit to lose its temper and dull and the material to work harden. One compounds the other and then as Jonnymac said "your screwed". I have seen them glow red and even 600f is to much. The temperatures at the very cutting edges of machine tools like end mills and lathe bits can be very high, that is why they are often M series steels or carbide. Normal drill bits can not stand these temps, cobalt does better but not at much higher temps. Running a bit fast and/or without good cutting oil is asking it to do the same the same as a high speed cutting tool and it will fail.
If your drilling all the way thru on a drill press have a hardwood backing under the work piece. I have little pieces of hardwood in a small box on the base of my drill press. I helps for when your bit goes thru and keeps you from drilling up your table or crossfeed vise.
Carbide is great, but I won't even put a carbide bit in my drill press. It is simply not rigid enough and has to much run out and even with the work clamped down solid, I will probably break a high dollar carbide drill. I only use my end mill to drill with carbide.