I finally figured out what the problem is: bad power steering pump. My wife had also mentioned that the steering was stiffer right around the time this began occurring, but it wasn't enough of a difference to really make a problem driving.

I found this video that shows the problem possibly being caused a bad O ring on the steering fluid intake, although I don't have any visible leaking. The $.68 part fixed the problem up to about 85%.

I'll be replacing the power steering pump later this week. Here is a DIY that I found on how to do that: Power Steering Pump Replacement DIY