How do I get my Danish Girlfriend in the US and allow her to work as well?

I have a girlfriend I met in Denmark while studying abroad. We are very serious but marriage or engagement is not an option yet. We would like to take our time and do it at the right time, but we can't be together if we don't. Our only options are marriage, engagement or she gets a temporary or permanent work visa for a job in which US citizens can't fulfill themselves. This is impossible to get. I don't know what my options are as we want to be together and live together but she would need to work while here but immigration rules do not permit. Do I have any alternative options? Can I talk to a state representative?