The most dangerous common problem for humans is current through the heart area - most specifically, through the nerves of the heart that control its muscle movements. A current of 10 to 20 mA may be sufficient to throw the heart into arrhythmia (did I spell that right?) and thus fail to keep blood supply flowing.
Almost right.
The main cause of death in accidental electrocution is cardiac arrhythmia, where the heart beats in an unsynchronised or excessively fast way, such that no, or almost no, blood gets pumped.
An electrical current though the heart can trigger a dangerous cardiac rhythm disturbance (most commonly discussed in this context is ventricular fibrillation, which is fatal within a couple of minutes). The risk of developing VF is dependent on the current and the length of time that the current is applied. Most guidelines state that a current of 30 mA through an adult torso, will have a negligible risk of triggering VF, provided that the current flow lasts less than 1 second. Below about 10 mA, there is essentially no risk. Above 30 mA, the "safe" time rapidly declines.
Most residual current devices/GFCIs are set to trip within 10 ms at a current of 30 mA. This provides more than adequate protection against VF. The problem with using more sensitive breakers, is that there is an unavoidable current flow between hot and earth, caused by the inherent capacitance of a wire. A large home with a 10 mA breaker at the service is likely to suffer unacceptably frequent false tripping, because of capacitative currents, and that's even with no appliances connected. A lot of appliances are naturally "leaky" - e.g. water heaters, as the ceramic insulation eventually degrades due to the heat, but such leakage is not harmful, provided that the heater is earthed.
Note that the figures are based upon current flow through the torso of an adult. Children and infants are potentially at higher risk - but as the major risk of electrocution is from damaged cables, and as children and infants tend not to use power tools (which are the major hazard) this is considered acceptable. As it is, the "instant" trip of a GFCI provides sufficient safety margin that even an infant would be unlikely to be harmed.
If the current flow is directed through the heart itself, you need very much less current (and voltage). A typical medical pacemaker has an adjustable voltage, but if the heart is reasonably healthy, you may only need a pulse of 100 mV or less, to stimulate the heart muscle.