My (U.S.) company has contractors that work in other countries (Canada, Chile). It's outside my domain, but I know that working with contractors is much easier than working with employees in other countries from an accounting point-of-view. Essentially we have only reporting requirements with contractors, but with employees we would have tax withholding and insurance requirements as well, and they would be unique to each country.
See if you can find contract work in the U.S. It would really help your case if you did the legwork on what would be required of them to use you as a contractor: What are the reporting requirements (Forms / Frequency / File Dates).
To hire contractors in the U.S., for instance, it requires only one annual 1099 form for each contractor, which must be submitted to the IRS and the contractor in January of each year if the total annual amount paid is $600 or more. That's what info you need to determine for your country.
Also, this doesn't apply to you in Europe, but make sure your country and the U.S. don't have software export restrictions or banking restrictions between one another.