"Icing of the indoor coil or the large insulated covered copper pipe. There are two main reasons for this, lack of air flow or low on refrigerant. Lack of air flow can be a dirty air filter, dirty indoor evaporator coil, dirty fan blades, damper in duct restricting air flow.
Keep blinds closed, curtains drawn, window shades down. A working attic fan would be a good idea. Plenty of insulation in the ceiling & walls. Air tight storm windows. Keep outside doors and openings close, etc.
Never leave the house and turn OFF the A/C. then come back home and turn it on and expect it to cool the house anytime soon. Doing this will not allow the unit to cool down the house for several hours. You can set the temperature up five to ten degrees but NOT OFF. This is because of Latent heat buildup in the walls and furniture in the house and will make the A/C work harder to remove the heat, this takes a long time.
"Doors" if you close the door to a room make sure that there is about a 3/4" gap between the bottom of the door and the floor. You may have had carpet put down on the floor and now there is no gap. This is necessary if you have a central return air duct in the hallway. The return air ducts need to pull the warm air from the room.
"Warm Rooms" on the lower levels of the house where it is cooler cut back / partially cut off some vent registers (Diffuser) but do not close them off all of the way, doing so could interfere with the static air pressure (air balancing of the system.) Make sure that all the ones on the upper floors where it is warmer are open all the way!
Never turn the A/C off than back on in less than five minutes, this will short-cycle the compressor and can trip breakers, blow fuses, or cause permanent damage the compressor. You should have a time-delay install on the A/C to prevent this during power outages! Most digital programmable thermostats have a time-delay of 3-5 minutes built-in. Having a start capacitor and relay is a good idea. This will increase the life expectancy of the compressor by starting faster thus keeping motor temperature down, using less electric to start.
If the small exposed 3/8" copper pipe connecting the inside unit with the outside unit is hot to the touch there can be several reasons why;
(a)    A/C is low on refrigerant.
(b)    The outdoor condenser coil is dirty.
These are the two most common reasons for it to be hot to the touch.