I've been involved in literacy programs since 1994 and can't agree that most Americans can't read well; but in some cities this is true. In Columbus OH, yearly numbers show over 50% of students drop out of high school - on the west side of town, the figure is 70% dropouts. Our large suburbs have much better rates of graduation and reading levels.
In the most recent national survey, the US found in the 2003 National Assessment of Adult Literacy that 13% (28 million) of all of us age 16 years and older read at the top level "Proficient" and 44% or 98 million read at "Intermediate." That's 126 million adults that read pretty well. Another 29% read at "Basic."
However, in 2010, different government and literacy agency sources state that 30, 42, or 44 million adult Americans are functionally illiterate. When I was testing people myself as late as the end of 2005, this meant reading at below the 4th grade reading level. I saw huge numbers of these clients as late as 2005.
Without looking into it further, I'd say we have a lot of people that can read very well and some, but not as many, that cannot read much at all. I also notice UN and UNESCO graphs showing literacy going down in Europe.
As for immigrants documented and undocumented, our churches in Central Ohio have taken the lead in teaching them English and helping them to gain documentation and citizenship. I'd have to say literacy is increasing among that group.