I too am having the same issue, and refreshing doesn’t help.
One thing I’ve noticed is that the plugin displays the Tweets properly on computers on which I’ve previously logged into Twitter. It displays “No Public Tweets” on all other computers that I’ve tried.
To test this, I cleared the cache and history of the browser on my computer and it showed the “No Public Tweets” message again.
I’m using version 1.3.8 of the plugin and 3.4.1 of WordPress, and I’ve double-checked that my Tweets are public.
Does anyone have suggestions?