Here's another option that occured to me. Because she's not your wife, it's ok to use deception and dishonesty.
Surely if you ask around you'll find that you know someone who knows someone who's nephew is a furnace repairman. Call the guy up, explain your situation, tell him that you're gonna tape a c-note inside the panel on your funace that you open to change the air filter. Tell him he can have that c-note if he'll just top by your house tomorrow evening after work in his furnace truck, wearing his uniform, go downstairs, bang on the ducts a bit, and come back upstairs and tell your girlfriend, "Well, bad news. The fratastat is completely plugged and the control circuit is burned out. They don't make that model anymore, so parts are hard to get. Besides, if I fixed it, I'd have to add the ultraviolet, infrared disinfecting retrofit kit. The law requires that these days ya know. Remember that case a couple of years ago of that whole family in Detroit that died of ebola from their humidifier? That was the same model you've got. Now, we've gotta put on the UV/IR kit whenever we fix on of those. All totalled, I'd be about $900. Of course, I could put a new unit on, but your furnace is an older model with an odd-size fitting. It'd cost a lot extra. Of course, we could rip the whole furnace out, but there's asbestos insulation in that model. It's no worry unless you disturb it. So, there'd be an extra charge for that. We'd have to tent the whole house. You'd have to move out for a week, maybe two, and we'd probably have to replace all the ducts too. Maybe you want to talk this over with your husband."
Don't forget to mention to your girl that because you love her so much, even though it might hurt your knives, you've arranged to have a furnace man come over this evening and fix the humidifier. Unfortunately, you've got to work a couple of extra hours this evening, so she'll have to let him in. When you get home and find her in tears because the humidifier is hopeless, you can say, "Cost is no object. If my baby wants a humidifer, we'll turn this house into a jungle. Where's that guy's number. We can stay at my mother's house while they tent ours for the asbestos removal."
Of course, she'll be the one to say no. And you can respond, "Well at least we're gonna get a room humidifer for you. And, if it's dry skin that's your problem, I'll personally apply lotion to every inch of your entire body twice a day. And then, you can do me."
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Chuck
Balisongs -- because it don't mean a thing if it ain't got that swing!
http://www.4cs.net/~gollnick