Setup Error

Try changing line 32 of lib/wp_twitteroauth.php from

public $ssl_verifypeer = TRUE;

to

public $ssl_verifypeer = FALSE;

If it works, it suggests the error tracks to how your server handles SSL.

This should solve the problem short-term, but be aware that Twitter are planning to switch off non-SSL connections in the future.

The latest development version of the plug-in should allow you to fix this via the settings page.