I have a similar Crapsman 1hp Drill Press model 113.213151 and mine has done it since brand new. (I didn't really use it for a few years or I would have returned it) I think it's the Quill tube that has too much free play in the cast head. To test this first release belt tension from drive belt or it will make bearings seem tighter than they really are if there's a problem, then lower the chuck 1" and with a bright light shining on the Quill jiggle the chuck from side to side and you should see the Quill move. Now lower the chuck all the way down and with downward pressure on it jiggle the chuck again. It doesn't move does it because the rack gear is exerting pressure on the quill holding it in place and stopping it from moving. If you back off 1/2" and try it again it should wiggle again even if you don't touch the chuck but only grab the bottom of the Quill. If it were the bearings it would still wiggle when held in the down position or when all the way up because they are inside the Quill Tube in my opinion. You can adjust some of this out by adjusting the screw on the left hand side of the cast head piece. My slot was so rough I had to clean it up first so the quill would still move up and down. Pretty crappy design and materials. There is a fine line between tightening up the slop and the Quill not moving. If you don't have a manual you can go to SEARS.com, go to tools and then PARTS. Type in the model number and you can view exploded parts diagrams. Here are some pics to try and make my post make more sense.
*I was going to just purchase another drill press but every one I tested did the same thing, when the Quill was lowered there is play at the chuck because of poor tolerances between the Quill and the casting. Go to the store and try it yourself on a brand new machine.
#1LOCKNUT M17 X 1.0 817309
#2 RING, LOCKING 817310
#3WASHER 817311
#4BEARING, BALL 17MM (SEE NOTE) STD315235 #5GASKET, QUILL 817535
#6TUBE,QUILL 817532
#7KEY, DRIFT 817326
#8KEY, CHUCK 817339
#9 CHUCK 817340
#10 ARBOR 817341
#11 SPINDLE 817531
#12 BEARING BALL (SEE NOTE) STD315245
