Assuming that you can find a gear reducer with an effective moment of inertia within the motor's range, you can probably crush soda cans with a 3v motor. At some point you're so geared down that the actual load is all but invisible to the motor, and you're simply driving the gear reducer. BUT, to crush a soda can this way, it might take an extremely long time.
It can take some effort to get this right. You might check out http://en.wikipedia.org/wiki/List_of_moments_of_inertia, and calculate the moment of inertia of a cylinder, maybe a quarter inch high with the density of copper and diameter of your hopper, as a first approximation of what you need to drive. The idea is that there will come a point where if you make your coin stack high enough, you won't be able to drive it. Of course, this is an approximation-- you're only trying to move the bottom layer of coins, and there's a mass sitting on top of that, yadda yadda yadda. We're ballparking here, not trying for an exact physical model.
To find the inertial range of a hobby motor, try http://www.mabuchi-motor.co.jp/en_US/product/p_0303.html. Mabuchi seems like a pretty typical "hobby" motor. Enter the diameter of the motor you're thinking about, and 3 Volts, and take a look at the ratings page that comes up. You're interested in the torque at maximum efficiency.
Do any unit conversions you need to do, and divide your cylinder moment of inertia multiplied by about 2-4 for a safety factor, divide by the inertia that the motor can drive from the mabuchi table, and that's the gear ratio you need for that motor. Look at the speed for that motor (in rads/sec), divide by the gear ratio, and thats how fast your coin disk will spin. If you're happy, go buy a motor/gearhead assembly to match. You can do this in any order -- start with the specs for the motor you'd like to buy, and calculate whether its good enough for you, start with a speed spec and make sure you meet it, etc.
If you can't get there with a "regular" gearhead, other options might be something like a planetary gear, which would be very geared down, or maybe a worm gear drive.
The opposite approach is to shop online, look for something that you think will work, buy it, wait for it to arrive, and see if it works. Repeat as necessary
The right approach for you lies in between these two extremes, and has to do with how much money you want to put into it, whether returns are possible, whether you need to go way overkill just to make sure you meet a deadline, and all sorts of other factors.
Lastly, look at the current specs for the motor you're about to buy, and spec out whether you can drive it without a driving circuit. As a guess, looking at some of the Mabuchi specs, I suspect you'll want something that can source about 300 mAmps to feel comfortable, maybe a half amp.