When this country began, we created programs and benefits to help populate, fill out, and explore this great country, e.g. the Homestead Act, and associated Homestead Acts.
In addition there are many laws protecting the labor, employment, and commerce of the U.S.
I believe unemployment in the U.S. has more to do with complacency, and reluctance to relocate, than it has to do with "jobs Americans don't want to do."
There is an argument to be made that alien's who do not have employment authorization are taking the U.S. jobs, but that has a lot to do with employers, and lack of punishment for employing those individuals.
Many LARGE employers actually pay unauthorized aliens, at and above local/state/federal regulations, with taxes being deducted as well. So the only difference is unauthorized aliens do not take such a thing for granted.
Why doesn't the Government create programs/initiatives to encourage people to move to these areas?
Ideas could include housing/property, and relocation expenses, with stipulations regarding length of residency, maintenance of employment, etc, much like the Home Buyer Tax Credit, had requirements like must be 1st home purchase, and 3 year primary residency requirement. Also Good Neighbor Next Door Program, or the Homestead Act which granted people land, so long as they filed an application, improved the land and filed for deed of title.
The government can also create a registration system for these individuals where people can apply for the programs and benefits.
When the Government finds that an employer, who is employing individuals who are not authorized to work in the U.S., they can provide information on how to contact/hire the applicants who have registered for these programs and benefits.
Think of it like a stimulus package. You spend money in the hopes it creates more in return.