Even though ActionScript 3 doesn't support multiline strings normally, there is a way to get the same result. Simply use the fact that you can declare XML inline, and call the text() method on the new XML instance. Here's an example:

var s : String = 
    <s>
        This is a heredoc
        style string.
    </s>.text();

'Course it doesn't matter what the root node's name is, it doesn't need to be used.
Also, don't forget that any text needs to be 'proper' XML. You could wrap it in CDATA tags, or use HTML entities. I'd recommend using entities, since you can still take advantage of embedded variables.