It's not possible; the browser does not treat HTML content inside of <script> tags as part of the DOM. When you retrieve the content of the <script> tag with $('#idhere').html(), you're getting a string result.
To answer Troy's question, he's most likely including templates in the <head> of his document so he can ultimately render content dynamically on the browser-side. However, if that is the case, the OP should use a different MIME type than text/html. You should use an unknown MIME type such as text/templates--using text/html confuses what the purpose of the content is.
I'm guessing the reason you're trying to reach into the <script> tag and grab a div is because you've built smaller sub-templates within the single <script> tag. Those smaller templates should rather be placed into their own <script></script> tags rather than contained in one large <script></script> tag pair.
So, instead of:
<script type="text/template" id="big_template">
<div id="sub_template_1">
<span>hello world 1!</span>
</div>
<div id="sub_template_2">
<span>hello world 2!</span>
</div>
</script>
Do this:
<script type="text/template" id="template_1">
<span>hello world 1!</span>
</script>
<script type="text/template" id="template_2">
<span>hello world 2!</span>
</script>
knockoutJsorHandlebarsfor example that is how you have to define the templates.