For a good discussion of the effects of minimum wages I can recommend this recent article in the The Economist which covered the subject quite well. Minimum wages are neither a panacea nor a job killer; they can act to correct perceived market failure: if people cannot live from their wages then some kind of subsidy is usually forthcoming. But if they are pushed too high then they will inhibit economic activity.
But with regards to automation minimum wages really are a side issue. Capitalism favours rationalised production lines wherever possible with competition encouraging either lower wages or automation of the lowest-skilled, most repetitive jobs.