Check the back gearing on that camelback drill. You do not state the manufacturer of the drill press. Back gearing was used on many camelback drills to give an extra slow range of drilling speeds. Different manufacturers of camelback drills used different designs of back gearing. It is the same principal of back gearing as is used on many "cone drive" (headstocks driven by belting and cone pulleys) lathes. Some makers of camelback drills used jaw (aka "dog") clutches to engage/disengage the back gearing. If you have the back gear clutches caught between "direct" (back gearing disengaged, cone pulley drives the spindle gearing directly) vs "back gearing 'in' (engaged, giving deep gear reduction), you will wind up with the spindle turning when there is no load on it. When you put load on the spindle such as drilling a hole, the spindle will stall.
There are other designs of back gearing used by the various manufacturers to get extra-deep gear reduction to the spindle. I believe one maker used a set of planetary gears adjacent to the step-cone pulley on the top shaft (horizontal shaft which has a bevel pinion gear to drive the spindle). The planetary reduction units often used a locking pin. If the pin was "in", the top cone pulley drove the top shaft/spindle directly with no further reduction. If the pin was "out", the planetary unit was engaged and added deep gear reduction between the top cone pulley and the spindle. If that pin was not properly positioned (neither "in" nor "out"), the top cone pulley will freewheel on the top shaft. Oil or grease in the gearing will provide enough drag to cause the spindle to turn, but when real load is applied, the spindle will stall.
My first guess is you do not have the back gears fully engaged nor fully disengaged. The other possibility, and no disrespect intended here, is that you left out a shaft key in your reassembly of that drill. If you left out a shaft key on something like a step cone pulley, and tightened the setscrew in that pulley, the drill spindle will turn, but will stall under light loads. The setscrew is providing enough friction to transmit enough power to turn the spindle, but will slip under any real load. If you missed installing a shaft key, and are relying on a setscrew to transmit the torque, it won't happen and you will wind up with a chewed-up shaft.
I tend to think your problem lies in the back gearing. To get the back gearing to engage or disengage on these older drills, particularly the ones with the jaw or dog clutches, you have to pull the belting by hand and work the back gear lever until the jaws on the dog clutch line up and fully engage. Similarly, if the drill uses a locking pin for pinning the bull gear to the top cone pulley (as is done on lathes) you have to make sure that pin is either fully "in" or "out". If the pin is "in" (locking the bull gear to the cone pulley), the drill is in "direct", the top cone pulley will drive the spindle thru the bevel gears. If the pin is "out", the cone pulley will freewheel on the top shaft until you shift the back gears into engagement. Do NOT attempt to work or shift the back gearing, whether it uses dog clutches, or moves a set of gears in and out of mesh, with the drill under power. Do not expect the back gearing to go smoothly in or out of engagement. Pulling the drill's top shaft over by hand while working the back gearing is usually what it takes. My guess is you moved the back gear lever and thought you had things engaged, only things are caught between back gears "in" or "out".