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) tanβ = 1; (iii) flavor non-universal, but automatically flavor-conserving soft scalar masses; (iv) a light colored scalar with peculiar phenomenology. The familiar μ problem looses its meaning in this approach.