I have a similar (but completely different!) goal, and after some trial and error ended up with a flat odometer road, fed with data via the api. @Scarabaea's suggestion of days-to-due is a good one.
Odometer roads default to using the last datapoint entered, which could be handy if you want to be able to get back on the road. Though as stated, overdue is overdue, and always a derailment, in which case 'max' or 'min' seems like what you want (depends which way up the graph is).
Turns out that I didn't have to worry about the road width, though that was my first thought too. For @patimen's use case, the road width would be the mechanism for the graph going blue-orange-red as the deadlines approach. So presumably a width of '1 day' would be the right setting.
I did indeed have to turn off accidental odometer resets, because my api regularly feeds it zeroes.