Well, I don't know delicious, but the code in the widget on your blog is this:
ious Links I Like</a></h3>
<div id="delicious-box" class="snap_preview" style="margin: 0pt; padding: 0pt; border: medium none;"> </div>
<script type="text/javascript" src="http://feeds.delicious.com/v1/json/philippaberrysmith?count=10"></script>
<script type="text/javascript">
function showImage(img){ return (function(){ img.style.display='inline'; }) }
var ul = document.createElement('ul');
for (var i=0, post; post = Delicious.posts[i]; i++) {
var li = document.createElement('li');
var a = document.createElement('a');
a.setAttribute('href', post.u);
a.appendChild(document.createTextNode(post.d));
li.appendChild(a);
ul.appendChild(li);
}
ul.setAttribute('id', 'delicious-list');
document.getElementById('delicious-box').appendChild(ul);
</script>
</div>
And of that the only thing I think may be a problem is the actual feed address. Is it indeed http://feeds.delicious.com/v1/json/philippaberrysmith ?
Because most feeds I deal with have /feed at the end, not at the beginning. Try putting that feed URL in an RSS widget and see if it displays that way.
Then again, there's a long shot that it only displays NEW posts to delicious, so try making one.