We use the level truncation scheme to obtain accurate descriptions of open
bosonic string field configurations corresponding to large marginal deforma
tions such as background Wilson lines. To do so, we solve for all fields as
functions of the massless string field, and confirm that the effective pot
ential of the massless field becomes increasingly at as the level of approx
imation is increased. Surprisingly, as a result of the merging of two branc
hes of the solution - one originating at zero tachyon vev and the other ori
ginating at the tachyonic vacuum - this effective potential exists only for
a finite range of values of the massless field. We use the D1 to D0-brane
marginal transition on a circle to explore the possibility that this finite
range corresponds to the infinite range of the conformal field theory para
meter describing marginal deformations, but are unable to arrive at a defin
itive conclusion.