yes but this is not a reflexive statement since today and day do not have equivalent meanings (eg tomorrow is also a day, and since tomorrow and today are not equivalent, neither one is wholly equivalent to day).
the obviousity is that “today” is clearly a subset of “day”.
and although the statement “today is a day” is not inherently a tautology, nevertheless the relationship between the two terms is so well established as to make its specification redundant.