It depends on what behaviour your real voltage supply might have.
If your real voltage supply is a battery it has a rather good defined internal resistance. LTspice allows you to model that if you edit the parameters of your voltage source.
If your real supply is a SMPS it gets more difficult. SMPS usually have shutdown procedures on overload. This must be modeled with some basic logic circuitry, e.g. using comparators and other means. You might resort to already modeled voltage monitoring circuits, but it might turn out complicated.
The third option, i.e. having a dual mode power supply with a constant voltage operating mode, which automatically switches over to a constant current mode on overload can be modeled the way Dave Tweed desribed.
But the first measure is to find out what the characteristics of your real PSU are.