  Modern extragalactic molecular gas surveys now reach the scales of
star-forming giant molecular clouds (GMCs, 20-50 pc). Systematic variations in
GMC properties with galaxy environment imply that clouds are not universally
self-gravitating objects, decoupled from their surroundings. Here we reexamine
the coupling of clouds to their environment and develop a model for 3D gas
motions generated by forces arising with the galaxy gravitational potential
defined by the background disk of stars and dark matter. We show that these
motions can resemble or even exceed the motions needed to support gas against
its own self-gravity throughout typical galaxy disks. The importance of the
galactic potential in spiral arms and galaxy centers suggests that the response
to self-gravity does not always dominate the motions of gas at GMC scales, with
implications for observed gas kinematics, virial equilibrium and cloud
morphology. We describe how a uniform treatment of gas motions in the plane and
in the vertical direction synthesizes the two main mechanisms proposed to
regulate star formation: vertical pressure equilibrium and shear/Coriolis
forces as parameterized by Toomre Q~1. As the modeled motions are coherent and
continually driven by the external potential, they represent support for the
gas that is distinct from that conventionally attributed to turbulence, which
decays rapidly and requires thus maintenance, e.g. via feedback from star
formation. Thus our model suggests the galaxy itself can impose an important
limit to star formation, as we explore in a second paper in this series.
