We present 12CO J = 1 → 0 observations of ultraluminous infrared galaxies (ULIRGs) obtained using the Redshift Search Receiver (RSR) on the 14 m telescope of the Five College Radio Astronomy Observatory. The RSR is a novel, dual-beam, dual-polarization receiver equipped with an ultra-wideband spectrometer backend that is being built as a facility receiver for the Large Millimeter Telescope. Our sample consists of 29 ULIRGs in the redshift range of 0.04–0.11, including 10 objects with no prior 12CO measurements. We have detected 27 systems (a detection rate of 93%), including 9 ULIRGs that are detected in CO for the first time. Our study has increased the number of local ULIRGs with CO measurements by ~15%. The CO line luminosity L'CO, correlates well with far-infrared luminosity LFIR, following the general trend of other local ULIRGs. However, compared to previous surveys we probe deeper into the low CO luminosity end of the ULIRG population as a single study by including a number of CO faint objects in the sample. As a result, we find (1) a smoother transition between the ULIRG population and local quasi-stellar objects (QSOs) in LFIR–L'CO ("star formation efficiency") space, and (2) a broader range of LFIR/L'CO flux ratio (~ 60–103 L☉/(K km s−1 pc2)) than previously reported. In our new survey, we also have found a small number of ULIRGs with extreme LFIR/L'CO, which had been known to be rare. The mid-IR color and radio-excess of 56 local ULIRGs as a function of FIR-to-CO flux ratio is examined and compared with those of spirals/starburst galaxies and low-z QSOs. In this paper, using a large sample of local ULIRGs we explore the origin of their current power source and potential evolution to QSOs.