  We identify a population of morphologically defined E/S0 galaxies lying on
the blue sequence at the present epoch. Using three samples, we analyze
blue-sequence E/S0s with stellar masses >10^8 Msun, arguing that individual
objects may be evolving either up toward the red sequence or down into the blue
sequence. Blue-sequence E/S0 galaxies become more common with decreasing
stellar mass, comprising <2% of E/S0s near the "shutdown mass" M_s ~ 1-2 x
10^11 Msun, increasing to >5% near the "bimodality mass" M_b ~ 3 x 10^10 Msun,
and sharply rising to >20-30% below the "threshold mass" M_t ~ 4-6 x 10^9 Msun.
The strong emergence of blue-sequence E/S0s below M_t coincides with a
previously reported global increase in mean atomic gas fractions below M_t for
galaxies of all types on both sequences, suggesting that the availability of
cold gas may be basic to blue-sequence E/S0s' existence. Environmental analysis
reveals that many sub-M_b blue-sequence E/S0s reside in low to intermediate
density environments. In mass-radius and mass-sigma scaling relations,
blue-sequence E/S0s are more similar to red-sequence E/S0s than to late-type
galaxies, but they represent a transitional class. While some of them,
especially in the high-mass range from M_b to M_s, resemble major-merger
remnants that will likely fade onto the red sequence, most blue-sequence E/S0s
below M_b show signs of disk and/or pseudobulge building, which may be enhanced
by companion interactions. We argue that sub-M_b blue-sequence E/S0s occupy a
"sweet spot" in stellar mass and concentration, with both abundant gas and
optimally efficient star formation, which may enable the formation of large
spiral disks. [abridged]
