We present the results of a survey of CO(1-0) emission in 14 infrared luminous dusty star-forming galaxies (DSFGs) at 2 < z < 4 with the NSF's Karl G. Jansky Very Large Array. All sources are detected in 12CO(1-0), with an angular resolution of ~1″. Seven sources show extended and complex structure. We measure CO luminosities of $(\mu ){L}_{\mathrm{CO}(1-0)}^{{\prime} }=0.4\mbox{--}2.9\times {10}^{11}$ K km s-1 pc2, and molecular gas masses of $(\mu ){M}_{{{\rm{H}}}_{2}}\,=1.3\mbox{--}8.6\times {10}^{11}$ M ⊙, where (μ) is the magnification factor. The derived molecular gas depletion times of t dep = 40-460 Myr, cover the expected range of both normal star-forming galaxies and starbursts. Compared to the higher -J CO transitions previously observed for the same sources, we find CO temperature brightness ratios of r 32/10 = 0.4-1.4, r 43/10 = 0.4-1.7, and r 54/10 = 0.3-1.3. We find a wide range of CO spectral line energy distributions (SLEDs), in agreement with other high-z DSFGs, with the exception of three sources that are most comparable to Cloverleaf and APM08279+5255. Based on radiative transfer modeling of the CO SLEDs we determine densities of ${n}_{{{\rm{H}}}_{2}}=0.3-8.5\times {10}^{3}$ cm-3 and temperatures of T K = 100-200 K. Lastly, four sources are detected in the continuum, three have radio emission consistent with their infrared-derived star formation rates, while HerBS-70E requires an additional synchrotron radiation component from an active galactic nucleus. Overall, we find that even though the sample is similarly luminous in the infrared, by tracing the CO(1-0) emission a diversity of galaxy and excitation properties are revealed, demonstrating the importance of CO(1-0) observations in combination to higher-J transitions.