As @mrdwab points out, save saves the names as well as the data/structure (and in fact can save a number of different R objects in a single file). There is another pair of storage functions that behave more as you expect. Try this:
saveRDS(df, file="mytweets.rds")
df2 <- readRDS("mytweets.rds")
These functions can only handle a single object at a time.
