Well, actually ten days of it! My local paper pointed out the week situation on their fB page. I didn't catch a source from them. But anyway check it out (in USA tradition of date writing):

4-10-14
4-11-14
4-12-14
4-13-14
4-14-14
4-15-14
4-16-14
4-17-14
4-18-14
4-19-14

My guessing is it won't happen again until the ten days of May next year for the 5-1x-15 period.

That's all quite nice for the American date style (m/d/yy). In Europe most people use the style d/m/yy or dd/mm/yyyy, so no chance for palindromic days in this specific period.

It is still a palindromic month, though...4/14.

The next palindromic days in Europe (d/m/yy) will be
4-10-14 (Oct 4)
4-11-14 (Nov 4)
4-12-14 (Dec 4)