I'd say unless the humi is going to be 100 sq feet or more you probably won't need an auto-fill option, unless you plan to be away from it for extended periods. I'm not really familiar with the humidifiers used in walk-ins, but if you really do want to go an auto-fill route, you should probably still use distilled water. Tap water will leave a mineral buildup over time as water cycles through it.
A quick search on walk in humidifiers turned up this one:
Link
Not sure what your budget looks like but that Humidifier isn't all that much more expensive than just buying a couple hydras for a cabinet. It does have an auto-fill feature, which you could hook up to a home distiller unit like like
this one. It has a dispenser pump option that would in effect be the same thing as tapping into a water line.
My father-in-law sells distillers (owns that website), so I could talk your ear off about those all day long.
I personally have
this one in my house right now. It's actually hooked up to an auto-fill setup for a Hydroponic Garden I have going. We also use it for normal drinking water. The tap water here in Reno is horrid, and if you knew half the stuff I know about what is in tap water (and even bottled water) you'd probably never touch the stuff again.
Even RO isn't all that great in comparison to distilled. Can't beat zero contaminants.
Anyway, if I was going to do it (and I'm sure I'll get there eventually), that would be the route I take.
-Chris