Get Width of 2d Game Object

Your question would be better titled "Get the Width of a PolyonCollider2D." Here is a some code to do that calculation and a bit more. The SetMinMaxPoly2D() function finds the world position of the four vertices on the path that are the minimum and maximum of an axes aligned box. Given what I believe you are trying to do, these are the points you need (at least on the x axis). If you need to calculate how far your collider extends to the left and right from the object pivot point you can do:

 var leftExtent = transform.position.x - minX.x;  
 var rightExtent = maxX - transform.position.x

The width of the collider is only going to help you if your polygon collider is symmetrical left and right across the pivot point.

This code calculates the four points each frame. It takes into account rotation and positioning. It places four small spheres at the found vertices. If you click the left mouse button, it will display the width and height (what your questions asked for).

 #pragma strict
 
 private var minX : Vector3;
 private var minY : Vector3;
 private var maxX : Vector3;
 private var maxY : Vector3;
 
 var marker : Transform[] = new Transform[4];
 
 function Start() {
     for (var i = 0; i < marker.Length; i++) {
         marker[i] = GameObject.CreatePrimitive(PrimitiveType.Sphere).transform;
         marker[i].localScale = Vector3(0.1, 0.1, 0.1);
     } 
 }
 
 function Update() {
     SetMinMaxPoly2D();
     marker[0].position = minX;
     marker[1].position = minY;
     marker[2].position = maxX;
     marker[3].position = maxY;
     
     if (Input.GetMouseButtonDown(0)) {
         var width = maxX.x - minX.x;
         var height = maxY.y - minY.y;
         Debug.Log("Width = "+width);
         Debug.Log("Height = "+height);
     }
 }
 
 function SetMinMaxPoly2D() {
     minX = Vector3(Mathf.Infinity,0,0);
     minY = Vector3(0,Mathf.Infinity,0);
     maxX = Vector3(-Mathf.Infinity,0,0);
     maxY = Vector3(0,-Mathf.Infinity,0);
 
     var poly = GetComponent(PolygonCollider2D);
     for (var i = 0; i < poly.pathCount; i++) {
         var path = poly.GetPath(i);
         for (var v : Vector2 in path) {
             v = transform.TransformPoint(v);
             if (v.x < minX.x) 
                 minX = v;
             if (v.y < minY.y)
                 minY = v;
             if (v.x > maxX.x)
                 maxX = v;
             if (v.y > maxY.y)
                 maxY = v;
         }
     }
     
     var z = transform.position.z;
     minX.z = z;
     maxX.z = z;
     minY.z = z;
     maxY.z = z; 
 }

If your object is never rotated or scaled and if you are only interested in the X extents, you can cut this code down a fair bit.