  Swift recently discovered an unusual gamma-ray and x-ray transient (Sw
1644+57) that was initially identified as a long-duration gamma-ray burst
(GRB). However, the ~ 10 keV x-ray emission has persisted for over a month with
a luminosity comparable to its peak value. The astrometric coincidence of the
source with the center of its host galaxy, together with other considerations,
motivated the interpretation that Sw 1644+57 was produced by an outburst from a
10^{6-7} M_sun black hole at the center of the galaxy. Here we consider the
alternate possibility that Sw 1644+57 is indeed a long-duration GRB, albeit a
particularly long one. We discuss the general properties of very long-duration,
low-power GRB-like transients associated with the core-collapse of a massive
star. Both neutron star (magnetar) spindown and black hole accretion can power
such events. The requirements for producing low-power, very long-duration GRBs
by magnetar spindown are similar to those for powering extremely luminous
supernovae by magnetar spindown, suggesting a possible connection between these
two unusual types of transients. Alternatively, Sw 1644+57 be associated with
the faintest core-collapse explosions: the collapse of a rotating red
supergiant in a nominally failed supernova can power accretion onto a
solar-mass black hole for up to ~ 100 days; the jet produced by black hole
accretion inevitably unbinds the outer envelope of the progenitor, leading to a
weak ~ 10^{49} erg explosion. In both neutron star and black hole models, a jet
can burrow through the host star in a few days, with a kinetic luminosity ~
10^{45-46} ergs/s, sufficient to power the observed emission of Sw 1644+57.
