The fast of the 10th of Teves is not pushed off.

 I see my husband blogged this topic about it 3 years ago.  See Divrei Chaim: 10 Teves and fasting on Shabbos:, which is linked to in this year's post at http://divreichaim.blogspot.com/2010/12/10-teves-fasting-for-future.html"