I've been following the Convert 2D to 3D video that is given in the Help section of AutoCAD 2012, and whenever I try to sweep the handle using the same methods that were used in the video it says that it is unable to sweep 1 selected object (when I select the path). I've attached the DWG file if that helps.
Also, when I went to use the 3D align feature I did exactly as the video did, but my handle wouldn't align with the side of the mug. It kept lining up with the side but never between the top and bottom of the mug like you'd expect. I kept having to move it to get it down where it needed to be.
Patchy, did you try sweeping the OP's original geometry?
There seems to be something peculiar about the OP's spline, as I can't sweep it in it's original state either. However if the "method" is changed from from Control Vertices, to Fit, in the Properties Palette, it sweeps fine, even after being changed back to the original setting.