You have to understand how the widget works. Your button is completely hidden from the view. widget.js hides it and replaces it with an iframe instead. So you can’t style it AFAIK.
With the other solution, you don’t even need to use the widget, you just build a url like this:
$('#tweet').attr('href', 'https://twitter.com/intent/tweet?text="' + YOUR_TWEET_TEXT_HERE + '");
See? You build a URL and just pass parameteres. All the related parameters are in the link above. What is more, you can now style your button however you want 
Notice: I think you’ll need to use target="_blank" to your link in order to work properly.