I've done something a little similar in the past, although in my case it wasn't around today, it was centred on the data of a report the user was working on, to help them find related reports in the surrounding few days, so there was less confusion with where today fell in the display.
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I think the trick is to make the past, present and future visually distinct. The past is greyed out a bit (if you can't edit that then it's doubly appropriate to do this). The present is highlighted, and the future is plain. The colour emphasis you'd want would vary depending on your application though. Think about which time period is more important to users - what are they just referring to versus actively working on. For example, if entering things in the past is a big part of the work, a pale yellow (for example) might be better than grey since that doesn't have the connotation of being "greyed out".
Today is labelled TODAY, rather than Friday, to make the model clearer. Having TODAY pop out by making it bigger (although presumably might want a time grid to line up) could also help to make it unique and therefore obviously important.
If this is useful in the application's context then any confusion will be short lived because the presentation will match the users needs, and it will be a pleasant surprise that the app is being helpful by providing something useful.
If you want people to understand the model clearly though, don't vary it. If on Sunday you showed the following week, but not today and the previous two days, then the whole display would be white, and the concept might be lost through a more unpredictable behaviour. Users may just be a bit confused as to why they couldn't see today.
Most calendars switch to a month view for longer periods of time, but you could help build a stronger mental model for your display if you let (if appropriate) people scan into the past or future using buttons either side. This could help reinforce the concept that time flows from the past on the left to the future on the right, and it's one long ribbon extending in both directions. The view you present is just a 7 day segment of that, not aligned to week start/end. Today as the 3rd day would then just be the initial position. If this is an interface people would use regularly then in time I'm expect people to know that white was future, and grey was past, so even if today wasn't in view, they'd still have some orientation, but that would only work if this interface was used heavily people. If it's something people only use once in a blue moon you couldn't rely on that.
