From the fancybox api docs:

$.fancybox.resize: Auto-resizes FancyBox height to match height of content.

So it looks like it is not intended to adjust the width.

If you wish to adjust the width, you can do it by manually resizing the #fancybox-wrap and #fancybox-inner elements. After some very quick checking, it looks like #fancybox-wrap is set to 20px wider than #fancybox-inner:

$('#fancybox-inner').width(400);

$('#fancybox-wrap').width(420);

You can also control the width when you first register fancybox using the width option:

$('#somelink').fancybox({ width: '100px' });