As far as the heart goes even a healthy person can't sustain more than a few mas of current for even short period of time, it has absolutely nothing to do with the health of the person it has everything to do with the nerves that transmit the hearts pacemaker signal from the brain being stunned into fibrillation or damaged to the point where a normal rhythm can't be restored in time due to nerve damage. No physical damage to the heart needs to occur for it to be lethal. This same thing can happen to breathing regulation.
As far as I²R heating goes this is NEVER good as body tissues don't generally like to be cooked =) However it is a separate issue from possible heart or breathing stoppage. Which is why even current limited high voltage electricty can be dangerous.
As far as tasers go they are VERY carefully current controlled. The intial voltage on them is incredibly high, something like 50-100kv's but current limited to prevent instant death, once the probes hit and intial high voltage starts conduction the taser automatically goes into lower voltage (few thousand volts) mode that is very low current designed (and quiet effective) at causing uncontrolled muscle contractions. The heart being in the center of the body is seldom in the direct path of the electricity so the danger to the important parts of the nervous system tend to be limited, however even a very safe taser can overwhelm someone with a weak heart or an otherwise compromised nervous system. There have been several reported deaths of people that were tased, sometimes long after the tasing actually occurred from nervous system shock.