I am also a machinist..... Yeah, use a drill press not a a hand drill. the drill press will give you a mechanical advantage through the quill handle.
I dont know about spring steel, but what one of the posters mentioned earlier is called work hardening. As Bronco said, if you dwell in the hole while the drill bit is spinning, but not actually cutting, it will either dull the bit or work harden the material or both.....
Set the drill press to the slowest setting it has. By my calcs you should run about 300 RPM for a 3/8 inch diameter hole. Use plenty of cutting oil. If you can get it, Moly-dee works good but is smelly and messy. The best stuff in the world IMO is Tapmatic EDGE tapping gel... Works on anything.
You can get carbide tipped drills and they will drill through almost anything if used properly. Just make sure it is a carbide tipped machine drill, NOT a masonry bit.
That is a whole different animal. If you try to drill steel with a masonry bit it will take you all day, a half dozen drill bits, and you would be lucky to go a 1/4 inch into the steel.....
Also, and this is for EVERYONE, NEVER, NEVER, EVER, hold the material by hand on a drill press. EVER!! USE C-CLAMPS, KANT TWIST, BESSYS, or PIPE CLAMPS if you have to, but NEVER hold it by hand. EVER! Trying to hold material by hand while drilling through it on a drill press is universaly stupid....Just my $.02