Here's my shot:

var cursor : Transform;

var horizontalSpeed = 10;
var verticalSpeed = 10;

function Update() {
    //Move the 3D cursor with the mouse

    var x : float = horizontalSpeed * Input.GetAxis ("Mouse X");
    var y : float = verticalSpeed * Input.GetAxis ("Mouse Y");

    cursor.transform.position = Vector3(cursor.transform.position.x+x, cursor.transform.position.y+y, cursor.transform.position.z);
}

Note: This will only move the cursor on the X and Y coordinates. It does not take into account anything else. You'll want to create a second camera to render only this cube. Make sure it's not rotated at all, and is located close to the cursor. You'll also want to play around with the initial speed values to get them just right.

Good luck, hope this helps somehow. :)

I don't think this will keep the mouse right under the cursor (even if I get it calibrated perfectly on one computer, I imagine it might get different results on a second), but it's probably the best way to solve this problem. Thanks a bunch!