I have tried several cables to charge this GPS and they all say that they are not compatible. What should I be looking for in a cable that WILL charge the Nuvi
It may not be the cable that is the problem, it may be the power source the cable is connected to, if the power source does not supply sufficient current (Amps or mA), then it will be incapable of powering the Nuvi and also charging the unit, try a different power source eg. a mains to 5V USB adapter of at least 1 Amp (1000 mA), a computer USB socket etc.
If the problem is due to the cable it may be that the Nuvi 61LM uses a dedicated cable, some units are supplied with a special USB cable that has an extra ID pin to handle charging
You could also try charging the unit using the supplied automobile 12V to 5V adapter