I had a 10 day running streak going until this evening when I decided to take a night off. Personally, I think running streaks are ridiculous. I think the record currently is 40 years of someone running at least a mile each day. To me running a mile is not considered a workout. I could have gone out tonight for less than 10 minutes to keep my running streak alive, but its not worth it.
Last night, I started feeling a little tired during my run and this morning the bottoms of my feet hurt. I knew today would be a great day to skip. Plus I was home with kids which means I was exhausted by the time they went to bed. Tonight was a good night to skip. Plus tommorow, I am able to go out for a run mid morning rather than waiting until the evening.
My advice to you with regards to a running streak. Keep at it until your body tells you to stop. If you are only going to do 1 mile when you usually do 3 just to keep the streak alive, I'd say skip it and enjoy the rest day.