Day 7 of Walking And...
 

I had been increasing speed and distance each day. Started at 20 minutes and got up to 37 minutes yesterday. I have been happy making progressand pushing a little further each day.

Well today I walked slower and struggled to reach 31 minutes. My legs feel heavy and are tired. Should I be concerned? Rest a day? Take an aspirin before I head out?

Soreness is pretty common when you start using your muscles in a novel way. If this is a significant increase in your recent activity levels, then it's probably DOMS (delayed onset muscle soreness). It's happened to me, too, when I started going on drastically longer walks.

People don't really think of walking as very strenuous, but if you've been sedentary it will actually build some muscle in your legs! An anti-inflammatory painkiller would probably help out, so I'd say give it a shot.
You'll probably feel better after a few days. DOMS in and of itself isn't dangerous, the problem with it (other than pain, obviously) is if you're doing something where it effects your form/control and you injure yourself.