Does anyone know any other way to determine who is logging into a system, tracking if worker is on the clock and physically there working? Time tracking is awful in the hourly service world, because a user can always have another user log in and out for them with a shared badges, a shared password, and generally only a fingerprint or some other bio object can determine that a worker is really that person doing the sign in or sign out, unless a manager micromanages the time tracking. Is there any defensible way to prove that a worker was physically there inexpensively without biometrics?
For a low cost, hacked up solution, I'd look at tracking something that someone would be loath to share with someone else or be without. For that, I'd look at their phones.
A simple WiFi access point that registers the MACs and IDs of devices on the network would work in your case, but it also has flaws. MACs and IDs can be modified, but it takes a little technical knowhow. You would also have to register/reregister the devices over time. Stores are starting to use this technique in order to track shoppers, so there is existing thought and technology surrounding this.
Other than that, you might have to look at the old-fashioned method: greet your workers.