It appears to want the more general version of the PlotRange
option (I'd consider this a small bug):
NumberLinePlot[3, PlotRange -> {{0, 20}, All}]
or
NumberLinePlot[3, PlotRange -> {{0, 20}, {0, 1}}]
and you can get an inkling of how the PlotRange option is used inside of NumberLinePlot by looking at
InputForm[NumberLinePlot[3]]
which yields
Graphics[{{RGBColor[0.24720000000000014, 0.24, 0.6], PointSize[Medium],
Directive[RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6]],
{Point[{3, 1}]}}}, AxesLabel -> {None}, Ticks -> {Automatic, Automatic},
FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}},
PlotRange -> {{0., 6.}, {0, 1}}, PlotRangePadding ->
{{Scaled[0.1], Scaled[0.1]}, {0, 1}}, AspectRatio -> 1/(10*GoldenRatio),
AxesOrigin -> {Automatic, Automatic}, Axes -> {True, False}, ImagePadding -> All, {}]