This probabily isn't going to help the original poster since this was asked some time ago, but I was having the exact same problem and when I searched for help I found this question, so my answer might help someone that ends up here with the same problem.
I was trying to use this jQuery plugin as well and I was having a hard time to get it working too. Spent hours checking the code and searching for help but always got to the conclusion that the code was correct, so I had no idea what was wrong. However, somehow, it then started working.
One thing I noticed was that if I had the call for the css file first and then the js files, it would show some weird thing in the place where it should have the "x" for deleting the tag. But if I called the js files first and then the css file, it would work perfectly.
This is the code I used:
<head>
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<script type="text/javascript" src="bootstrap-tagmanager.js"></script>
<link href="bootstrap-tagmanager.css" rel="stylesheet" type="text/css">
</head>
<body>
<input type="text" name="products" placeholder="Add your Products" class="tagManager">
<script>
jQuery(".tagManager").tagsManager();
</script>
</body>
Hope this helps someone.