The standard javascript Twitter buttons execute their script on page load and then never again. You are out of luck if you want to programmatically change parameters later. (such as setting the "URL to tweet") The work-around is to instead use the iframe version of Twitter buttons and use query parameters to set options.

<iframe id="twitFrame" allowtransparency="true" frameborder="0" scrolling="no" src="//platform.twitter.com/widgets/tweet_button.html?url=http%3A%2F%2Fanders.com%2F&count=none" style="width:130px; height:20px;"></iframe>

Then change the iframe's src programmatically later to set options on the fly via jQuery. Here I change the URL to http://example.com/.

$( '#twitFrame' ).attr( 'src', '//platform.twitter.com/widgets/tweet_button.html?url=http%3A%2F%2Fexample.com%2F&count=none' );