You probably need to give us more information (What do you mean the facebook button isn't working? Are you getting an error message? If so, what? What are your logs saying?)
BUT, there's a good chance this is your problem: there is a known issue using omniauth facebook authentication on heroku. You need to add an explicit reference to the SSL certificates file in the config/initializers/omniauth.rb file. Change your facebook config line to include the 'client_options' hash like so:
provider :facebook, 'YOUR_APP_ID', 'YOUR_SECRET_KEY',
{:scope => 'PERMISSION_1, PERMISSION_2, PERMISSION_3...', :client_options => {:ssl => {:ca_file => '/usr/lib/ssl/certs/ca-certificates.crt'}}}
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