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, {}]