We present MAMBO 1.2mm observations of 40 extragalactic sources from the Spitzer First Look Survey that are bright in the mid-infrared (S_24um>1mJy) but optically obscured (log_10 (nu F_nu (24um))/(nu F_nu (0.7um))>1). We use these observations to search for cold dust emission, probing the similarity of their spectral energy distributions to star forming infrared galaxies or obscured AGN. The sample as a whole is well detected at mean S_1.2mm=0.74+-0.09mJy and S_1.2mm/S_24um=0.15+-0.03. Seven (three) of the sources are individually detected at >3sigma (>5sigma) levels. Mean millimeter fluxes are higher for sources with the reddest mid-infrared/optical colors. Optically faint but with relatively low mm to mid-infrared ratio, the typical SEDs are inconsistent with redshifted SED shapes of local star-forming infrared galaxies. They also differ from SEDs of typical submillimeter selected galaxies, with the 24um sources that are individually detected by MAMBO possibly representing intermediate objects. Compared to star-forming galaxies, a stronger but optically obscured mid-infrared component without associated strong far-infrared emission has to be included. This component may be due to luminous optically obscured AGN, which would represent a significant part of the high redshift AGN population.
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