  (Abridged) We develop and test a model for the cosmological role of mergers
in the formation and quenching of red, early-type galaxies. Making the ansatz
that star formation is quenched after a gas-rich, spheroid-forming major
merger, we demonstrate that this naturally predicts the turnover in the
efficiency of star formation at ~L_star, as well as the observed mass
functions/density of red galaxies as a function of redshift, the formation
times of spheroids as a function of mass, and the fraction of quenched galaxies
as a function of galaxy and halo mass, environment, and redshift. Comparing to
a variety of semi-analytic models in which quenching is primarily driven by
halo mass considerations or secular/disk instabilities, we demonstrate that our
model and different broad classes of models make unique and robust qualitative
predictions for a number of observables, including the red fraction as a
function of galaxy and halo mass, the density of passive galaxies and evolution
of the color-morphology-density relations at high z, and the fraction of
disky/boxy spheroids as a function of mass. In each case, the observations
favor a model in which galaxies quench after a major merger builds a massive
spheroid, and disfavor quenching via secular or pure halo processes. We discuss
a variety of physical possibilities for this quenching, and propose a mixed
scenario in which traditional quenching in hot, massive halos is supplemented
by the feedback associated with star formation and quasar activity in a major
merger, which temporarily suppress cooling and establish the conditions of a
dynamically hot halo in the central regions of the host, even in low mass
halos.
