  The second-order term of the approximate stress-energy tensor of the
quantized massive scalar field in the Bertotti-Robinson and Reissner-
Nordstr\"om spacetimes is constructed within the framework of the
Schwinger-DeWitt method. It is shown that although the Bertotti- Robinson
geometry is a self-consistent solution of the ($\Lambda =0$) semiclassical
Einstein field equations with the source term given by the leading term of the
renormalized stress-energy tensor, it does not remain so when the
next-to-leading term is taken into account and requires the introduction of a
cosmological term. The addition of the electric charge to the system does not
change this behavior. The near horizon geometry of the extreme
quantum-corrected Reissner-Nordstr\"om black hole is analyzed. It has the
$AdS_{2} \times S^{2}$ topology and the sum of the curvature radii of the two
dimensional submanifolds is proportional to the trace of the second order term.
It suggests that the "minimal" approximation should be constructed from the
first two terms of the Schwinger-DeWitt expansion.
