So like the whole of this world is stuck at 20 below ambient?+
Rule of thumb is that a modern air conditioner can maintain about 30F difference between inside and outside for a reasonably-sized system. If you drastically oversize the system, you can maintain a higher difference, but that costs more up-front, and also increases your run costs in terms of energy usage (that's not ALWAYS true, but for most cases, it is). Older systems typically do about 20F.
The reason depends on a number of things.
Remember that an A/C system is nothing more than a heat-mover. It takes heat from one place and moves it to another. It does this by absorbing heat at one point (the condenser), and rejecting it to another point (the evaparator).
Physics dictates that when you take a gas and compress it, the gas gets hotter. This is because you have taken all the energy in the gas and confined it in a smaller space (because you compressed the gas). Likewise when you take a gas and expand it, the temperature drops because now the energy is more spread out.
A compressor+expansion-valve allows you to take advantage of this fact by create a pressure differential in the system. The compressor pumps out high pressure (and hot) gas that goes to the condenser to cool off, then gets pushed through a metering valve that allows only a little gas at at time to come through, thus causing the gas to expand and cool off.
If you are really clever with the pressures you use on the high and low side of the system, you can actually compress the hot gas so much that when it goes through the condenser, it actually loses enough heat to become a liquid (hence the name "condenser"), and when you let the liquid dribble out through the expansion-valve into the evaporator it absorbs heat and evaporates, becoming a gas (hence the name "evaporator") and going back to the compressor to start the cycle all over again.
The really clever bit to all of this is that for any fluid that can be sufficiently controlled to go through both a gas phase and a liquid phase, the phase transition from gas to liquid and vice-versa absorbs/releases a LOT of energy, and the boiling point of the fluid can be varied by how much pressure (or vacuum) it is under.
Consider:
It takes 1 calorie of heat to raise 1cc (1 mL) of water 1 degree celcius.
It takes 280 calories of heat to convert that same 1cc of water into steam (a phase transition).
For our purposes, the rub of using water is that, well, it boils at 100C, which is rather too hot to be useful, and getting the boiling point low enough to be useful requires a near vacuum.
So we use refrigerants that have useful boiling points:
The most common commercial refrigerant in use today (R410A) has a boiling point of -48.6C at atmospheric pressure (1 bar). By increasing the pressure to about 15 bar (225 PSI) we can increase the boiling point to around 50C in the condensor.
In most systems, they will design the evaporator to run at about 7C in order to keep frost from developing and clogging the evaporator, but for e.g. freezers, they can go much lower.
The tradeoff, though, is that the greater the temperature differential you want to maintain, the bigger the system needs to be. This is why A/C systems are sized in terms of BTUs; the more heat you want to move, the bigger the system you need.
Also, remember that I said that most A/C systems run the evaporator at about 7C to prevent freezing. You also have to bear in mind that there is a finite period of time required to move heat from the evaporator into the surrounding air. This means that systems are designed to assume about 11C drop across the evaporator (in other words, your 7C evaporator will produce 20C air). But that's under IDEAL conditions, where the condenser is able to reject its designed heat load. But that assumes an ambient of about 30C (86F), because you have another 11C drop across the condenser to dump the heat into the air. That's getting to 41C, which is only a little below 50C (the condenser design temperature), which means that if the outside temp gets much above about 35C ( 95F) the system can no longer maintain a comfortable temperature.
Hope that clears things up (it probably doesn't).