The OP said the drill kicks on&off on occasion. The key here is that it does not trip the breaker, meaning he has an open in that extension cord or the drill press has a loose wire that intermittently opens causing the drill press to power cycle. If the power cord were to cause a large voltage drop it should be warm to the touch, also he could verify the resistance of that extension cord.
To the OP, does the drill press have the same issue when it is plugged directly into the wall? If the issue is in the drill press it is a very simple circuit, power cord enters, one leg goes to the 110v switch, from the switch it goes to your 3/4hp motor (that is a 9amp motor). The other leg goes straight to the motor. If you wanted to verify drill press integrity you could always measure the curcuit resistance 120v/9a=13ohms when you push the power button on, open when you push the power button off.
BFBOB has a good explanation on how to use a DMM to troubleshoot the system.
Please keep us posted on what you find, good luck & have fun.