Q:

How do I recreate this sweeps nurbs model in Three.js? 

In Cinema4d, this model is made using two circles in a sweeps nurbs.   One circle is the contour spline, and it sweeps along the other circle path.   With Sweep Nurbs you can specify the start and stop completion percentage and scale etc. 

Is there a way to reproduce this in Three js?   I suppose I can export this to an STL, but I'd much rather a way for 3.js to manage this itself. 
update:
I set a series of CircleGeometry to rotate around with this effect. 

var startR = .6,
    incR = .0049;

for (var p = 0; p < 110; p++) {
    var r = startR - (incR * p);
    var geometry = new THREE.CircleGeometry(r, 12);
    var material = new THREE.MeshBasicMaterial( { color: 0x000000 } );
    material.side = THREE.DoubleSide;
    geometry.applyMatrix( new THREE.Matrix4().makeTranslation( -7, 0, 0 ) );

    var circle = new THREE.Mesh( geometry, material );
    circle.rotation.y += p * 0.05

    scene.add(circle);
}

So maybe the next step is to combine these circle geometries in to one object? 

A:

If I get you right, then you can just bend a cone. 
Create a cylinder geometry.  It has radiusTop (r1), radiusBottom (r2).  Its height is equal to the angle of bending (theta).  Also we need the radius of bending (rMain).  After you created the geometry, translate it to the point of (rMain, theta / 2, 0).  And after all, apply such transformation for each vertex in the geometry that its new position is in polar coordinates, where radius is x-value and angle is y-value. 
function bendTheCone(r1, r2, rMain, theta, segments){
  var geom = new THREE.CylinderBufferGeometry(r1, r2, theta, 16, segments);
  geom.translate(rMain, theta / 2 ,0);
  var position=geom.position;
  for(var i=0; i<position.count;i++){
    var localTheta = position.getY(i);
    var localRadius = position.getX(i);
    position.setXY(i,Math.cos(localTheta) * localRadius,
      Math.sin(localTheta) * localRadius);
  }

  geom.computeVertexNormals();

  return geom;
}

Then you can use it like this:
var geometry = bendTheCone(0.1, 0.5, 10, THREE.Math.degToRad(320), 60);
var mesh = new THREE.Mesh(geometry, new THREE.MeshNormalMaterial());
scene.add(mesh);

jsfiddle example

