I'm struggling to understand why does this doesn't work.
df <- data.frame(a=1:10, b=1:10)
foo <- function(obj, col) {
   with(obj, ls())
   with(obj, print(col))
}
foo(df, a)
[1] "a" "b"
Error in print(col) : object 'a' not found
If this does work:
with(df, print(a))
                with is handy and improves readability in an interactive context but can hurt your brain in a programming context where you are passing things back and forth to functions and dealing with things in different environments.  In general within R, using symbols rather than names is a sort of "semantic sugar" that is convenient and readable in interactive use but mildly deprecated for programming [e.g. $, subset]). If you're willing to compromise as far as using a name ("a") rather than a symbol (a) then I would suggest falling back to the simpler obj[[col]] rather than using with here ... 
So, as a self-contained answer:
foo <- function(object,col) {
   print(names(object))
   print(object[[col]])
}
If you wanted to allow for multiple columns (i.e. a character vector)
foo <- function(object,col) {
   print(names(object))
   print(object[col])
}
edit: refraining from  using subset with a function, at @hadley's suggestion
(this will print the answer as a data frame, even if a single column is selected, which may not be what you want).
Anything that is passed to a function must be an object, a string or a number. There are two problems with this:
What you want is more like:
foo <- function(obj, col) {
       print(with(obj, ls()))
       with(obj, print(obj[[col]]))
    }
foo(df, "a")
Or if you're only looking for the one column to be printed:
foo <- function(obj, col) {
           with(obj, print(obj[[col]]))
        }
foo(df, "a")
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