Aaah, OK. Max isn't an out-and-out Solid Body editor, but it isn't the end of the world.
It sound like an option was left unticked with the original file export, which is why Max is struggling to import the object, but if Rhino has rectified that, then it's not a problem anyway.
If you're using Max purely for animating / rendering, can you delete the unneeded parts in Rhino first, before importing?
Back in Max though, I found the best way to work is to select the object in question, and under Viewport Display Settings (in the Modifier tab), select the Mesh radio button, then turn the quality to Coarse. If the mesh is still too dense in your viewport, you can adjust the Face Distance % to a higher number. You see live feedback when you adjust.
Obviously, you don't want it render like that, so make sure in Render Approx, that Use Viewport Mesh is unticked and Production is selected. Again, you can make the render tessellation even more fine by adjusting numbers underneath.
So even though Max doesn't have a convert-to-NURBS option (that I'm aware of), the above should make selecting the object easier (as you can see the edges to click on) and navigating the viewport and moving the object should be far more smoother.
There may be plug-ins that can convert, like Power NURBS Pro, but I genuinely don't need to.