This Letter addresses a provocative question: ``Can the standard electroweak
Higgs doublets and their color-triplet partners be the messengers of a low
energy gauge-mediated SUSY breaking?" Such a possibility does not seem to be
immediately ruled out. If so, it can lead to a very economical scheme with
clear-cut predictions quite distinct from those of the conventional
gauge-mediated scenario. Namely, we get (i) a single light Higgs below the
original SUSY- breaking scale; (ii) tan(beta) = 1; (iii) flavor non-universal,
but automatically flavor-conserving soft scalar masses; (iv) a light colored
scalar with peculiar phenomenology. The familiar mu problem looses its meaning
in this approach.Comment: 10 pages, LATEX, no figure