How difficult is it for someone who has aspergers syndrome to get a job with responsibility?

Asperger. Depending on onset & severity & education background, not at all difficult, as long as co-workers are supportive.
Spectrum Disorder. Asperger's syndrome is classified as a spectrum. In other words the severity of the illness has a broad range. At one end, the individual may be greatly impaired and unable to work at all. At the other end, the individual may be considered normal. So yes it is possible for an individual with asperger's syndrome to get a job with responsibility, but not every asperger's individual is capable.