Personally, I think that immigration and total unemployment are not correlated in any sensible way. These new "millions" will need food, clothes, utilities and everything a living human being needs. They will create demand for these, hence jobs, which they (or U.S. citizens) will later be able to fill. They will also not rely upon the U.S. government for support, as they have signed these rights off when applying, and will instead support themselves or have petitioner support them (by being productive members of society, i.e. holding a job or operating a business).
Also, personally, speaking of the unemployment rate of the U.S. citizens alone, do you think it is globally better for the economy if a less competent person gets to do the job instead of a more competent and qualified one, just because the former is the U.S. citizen?