I think you may be hinting at my answer in your own question. Why not show today's text by default, and let them pick other days using your dialog?
Okay, I whipped up a Windows form for you after my comment about adding a gesture to go to today's date. Your comment about polluting the screen with a button to achieve this made me think about how "polluted" the screen might be just by adding a button. Personally, I don't really think using the entire screen for text is very appealing--you need some margins, etc. or it looks like smashed ants.
You probably don't have a title bar, but if you did you could put your app name or the date the user is on. I did add the date the user is on above the "Lorem" where your text would go. The buttons on the bottom don't seem too obtrusive to me, but I guess it's a matter of personal preference.