First off, I’d really like to give a shout-out to the brave people who have created and maintain this great package – the fame is yours!

So, while exploring the capabilities of the package some issues with the ITIS-Server arose and with large datasets things weren’t working out quite well for me.
I then switched to the NCBI API and saw that the result is much better here (way quicker, on first glance also a higher coverage).
At the time there is no taxize-function that will pull taxonomic details from a classification returned by NCBI, that’s why I plugged together a little wrapper – see here:

# some species data:
spec <- data.frame("Species" = I(c("Bryum schleicheri", "Bryum capillare", "Bryum argentum", "Escherichia coli", "Glis glis")))
spl <- strsplit(spec$Species, " ")
spec$Genus <- as.character(sapply(spl, "[[", 1))

# for pulling taxonomic details we'd best submit higher rank taxons
# in this case Genera. Then we'll submit Genus Bryum only once and 
# save some computation time (might be an issue if you deal 
# with large datasets..)

gen_uniq <- unique(spec$Genus)

# function for pulling classification details ("phylum" in this case)
get_sys_level <- function(x){ require(taxize)
                              a <- classification(get_uid(x))
                              y <- data.frame(a[[1]])                                        # if there are multiple results, take the first..
                              z <- tryCatch(as.character(y[which(y[,2] == "phylum"), 1]),    # in case of any other errors put NA
                                            error = function(e) NA)
                              z <- ifelse(length(z) != 0, z, NA)                             # if the taxonomic detail is not covered return NA
                              return(data.frame(Taxon = x, Syslevel = z))
                             }

# call function and rbind the returned values 
result <- do.call(rbind, lapply(gen_uniq, get_sys_level))
print(result)
#         Taxon       Syslevel
# 1       Bryum   Streptophyta
# 2 Escherichia Proteobacteria
# 3        Glis       Chordata

# now merge back to the original data frame
spec_new <- merge(spec, result, by.x = "Genus", by.y = "Taxon")
print(spec_new)
#         Genus           Species       Syslevel
# 1       Bryum Bryum schleicheri   Streptophyta
# 2       Bryum   Bryum capillare   Streptophyta
# 3       Bryum    Bryum argentum   Streptophyta
# 4 Escherichia  Escherichia coli Proteobacteria
# 5        Glis         Glis glis       Chordata
#