To expand on what Wifi said, propane can be kept in the liquid state if maintained under pressure in the tank. Pressure goes up with temperature of the liquid. Here are some values (source:
http://www.flameengineering.com/Propane_Info.html):
Temp (F) Pressure (psig)
-30 6.8
0 24.5
70 110
100 177
[edit: I tried to insert more space between T and P values, to no avail. How do I do this?]
Inside the tank, the vapor space above the liquid level is vaporized propane. Thus it is possible for an outside tank to provide just enough pressure to deliver propane gas to the furnace. As the the gas is used, pressure drops slightly, more liquid is vaporized, and heat to vaporized more liquid comes from the liquid itself, cooling the liquid slightly. As the liquid temperature drops, heat flows from the warmer outside air temperature into the tank, and ultimately the liquid temperature won't drop anymore as steady state is reached. Under some conditions of humid air and something inside using propane, the level of liquid in the tank can be seen from the extent of condensation on the outside of the tank, much as it would be seen on a partially emptied cold can of beer on a humid day.
On the other hand, natural gas is mostly methane. For methane, tanking it is more complicated. Its critical temperature is about -117 F, at which temperature the pressure it exerts in a tank is 652 psig. This is the maximum temperature at which methane can have a liquid phase under any pressure. Any warmer (ok, less cold) than that and all you have is just compressed vapor at any pressure. Furthermore, as the critical temperature is approached, the densities of the vapor and liquid phases get closer and closer. To gain the storage volume advantage of a liquid, the temperature of methane must be kept very, very cold. For storage in a tank near atmospheric pressure, this temperature is about -260 F. Doing this is not practical for a domestic installation.