You can do this using a numbered list paragraph style and just use an empty paragraph for the day number. In the numbering options enter the text Day and a space before the number marker.
If you put this on the master page my recollection is you will need to override the frame on the document page to have the numbers update properly.
You can start a section on the page that will be Day 1, and then use page numbering on your master page.
Day <current page number>
That would work only if I had one section per page, right? I will have several sections so section number can not be the same as page number.
Thanks. I tried it and it worked for the first two pages, I was really happy.
Then I applied it to all my sections in the masters and began creating pages applying the masters... and suddenly all the sections were "Day 1" again and would not update and start counting even if I override the pages. :/ Not sure what happened there.