We present the results of an Australia Telescope Compact Array (ATCA) survey for intraday variability (IDV) of the total and polarized flux densities of 118 compact, flat-spectrum, extragalactic radio sources from the Parkes 2.7-GHz Survey. A total of 22 total flux density IDV sources were discovered and 15 sources were found to show IDV of their polarized flux density. We discuss the statistical properties of the IDV sources, including the distribution of source modulation indices, and the dependence of the variability amplitude on source spectral index and on Galactic position. We suggest interstellar scintillation (ISS) in the Galactic interstellar medium as the most likely mechanism for IDV. Even so, the inferred high brightness temperatures cannot be easily explained.