We describe a search for dust created in collisions between the Saturnian irregular satellites using archival Spitzer Multiband Imaging Photometer observations. Although we detected a degree-scale Saturn-centric excess that might be attributed to an irregular satellite dust cloud, we attribute it to the far-field wings of the point spread function (PSF) due to nearby Saturn. The Spitzer PSF is poorly characterized at such radial distances, and we expect PSF characterization to be the main issue for future observations that aim to detect such dust. The observations place an upper limit on the level of dust in the outer reaches of the Saturnian system, and constrain how the size distribution extrapolates from the smallest known (few km) size irregulars down to micron-size dust. Because the size distribution is indicative of the strength properties of irregulars, we show how our derived upper limit implies irregular satellite strengths more akin to comets than asteroids. This conclusion is consistent with their presumed capture from the outer regions of the Solar system.