  The 12CO J=4-3 to J=13-12 lines of the interstellar medium from nearby
galaxies, newly observable with the Herschel SPIRE Fourier Transform
Spectrometer (FTS), offer an opportunity to study warmer, more luminous
molecular gas than that traced by 12CO J=1-0. Here we present a survey of 17
nearby infrared-luminous galaxy systems (21 pointings). In addition to
photometric modeling of dust, we modeled full 12CO spectral line energy
distributions from J=1-0 to J=13-12 with two components of warm and cool CO
gas, and included LTE analysis of [CI], [CII], [NII] and H2 lines. CO is
emitted from a low-pressure/high-mass component traced by the low-J lines and a
high-pressure/low-mass component which dominates the luminosity. We found that,
on average, the ratios of the warm/cool pressure, mass, and 12CO luminosity are
60 +/- 30, 0.11 +/- 0.02, and 15.6 +/- 2.7. The gas-to-dust-mass ratios are <
120 throughout the sample. The 12CO luminosity is dominated by the high-J lines
and is 4 $\times 10^{-4}$ LFIR on average. We discuss systematic effects of
single-component and multi-component CO modeling (e.g., single-component J < 3
models overestimate gas pressure by ~ 0.5 dex), as well as compare to Galactic
star-forming regions. With this comparison, we show the molecular interstellar
medium of starburst galaxies is not simply an ensemble of Galactic-type GMCs.
The warm gas emission is likely dominated by regions resembling the warm
extended cloud of Sgr B2.
