How can a fridge water line be connected to a water jug

When you push the levers in to dispense water/ice, do you hear the motor running (but nothing comes out)? If so, then it's probably a supply problem (iced up line, etc). If not, then it's likely an electrical problem. Most likely a fuse or a bad relay.

To get into the unit, you would (usually) need to remove the whole plastic panel on the inside of the door. The screws are usually hidden underneath the seal that runs around the edge of the door. Your user manual might have some useful information as well.

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this GE document specifies a water pressure of 40-120 psi, for the ice maker to function properly.

• The water pressure must be between 40 and 120 psi.
• Pressures below 40 psi may cause a malfunction of the icemaker (i.e. producing hollow cubes or no ice production).

Which as BMitch points out in chat would mean the 1-2 gallon container would have to be about 100 ft. above the fridge.

Tester101: How tall would a 1/4" tube have to be, to produce 40 psi at the bottom if it was filled with water?

BMitch: if the link I found is correct, 93 feet