  The 100-m Robert C. Byrd Green Bank Telescope (GBT) and the Owens Valley
Radio Observatory (OVRO) 40-m radio telescope have been used to conduct a
survey of 3165 known extragalactic radio sources over 143 square degrees of the
sky. Target sources were selected from the NRAO VLA Sky Survey in fields
observed by the Cosmic Background Imager (CBI); most are extragalactic active
galactic nuclei (AGN) with 1.4 GHz flux densities of 3 to 10 mJy. The resulting
31 GHz catalogs are presented in full online. Using a Maximum-Likelihood
analysis to obtain an unbiased estimate of the distribution of the 1.4 to 31
GHz spectral indices of these sources, we find a mean 31 to 1.4 GHz flux ratio
of 0.110 +/- 0.003 corresponding to a spectral index of alpha=-0.71 +/- 0.01 (S
~ nu^alpha); 9.0 +/- 0.8 % of sources have alpha > -0.5 and 1.2 +/- 0.2 % have
alpha > 0. By combining this spectral index distribution with 1.4 GHz source
counts we predict 31 GHz source counts in the range 1 mJy < S_31 < 4 mJy,
N(>S_31) = (16.7 +/- 1.7) deg^2 (S_31/1 mJy)^(-0.80 +/- 0.07). We also assess
the contribution of mJy-level (S_1.4 < 3.4 mJy) radio sources to the 31 GHz CMB
power spectrum, finding a mean power of ell (ell+1) C^src_ell/(2 pi) = 44 +/-
14 micro-Kelvin^2 and a 95% upper limit of 80 micro-Kelvin^2 at ell = 2500.
Including an estimated contribution of 12 micro-Kelvin^2 from the population of
sources responsible for the turn-up in counts below S_1.4 = 1 mJy this amounts
to 21 +/- 7 % of what is needed to explain the CBI high-ell excess signal, 275
+/- 63 micro-Kelvin^2. These results are consistent with other measurements of
the 31 GHz point source foreground.
