Something like this:
Where the user would click on any area of the but
Have you tried using the LABEL tag? For accessibility sake we should be using label tags to associate labels to form controls all of the time. Not only does that help tie things together for screen readers, but it also makes the label as well as the control clickable.
You can read a bit more detail and find an example here: http://webaim.org/techniques/forms/screen_reader#labels