I have found that is impossible to make a point bigger than canvas horizontal size event forcing it setting in the glsl vertex shader the gl_PointSize to a value bigger than canvas width.
In this fiddler you can check it.
Just be sure you are using a canvas size in which width will be bigger than height. (4:3)
You can click at any point and controls.target will be set to the center of point and then zoom in.
Or you can manually force it by setting the gl_PointSize to a big value more than 2000.
Here a screenshot showing the problem: