I knew that was going to be your response. However, I've been down that road. The answer I get is, "oh, I do want to hang out. I've just been busy." A week later. Same question. Same response. And I get dragged on for weeks until she finally decides to say what the truth was all along and she just felt bad telling me. Doing it my way forces her to either let it go because it doesn't really matter or act concerned that we haven't spoken. You get a truer response when someone is obligated to make the first step. At least that's how I've seen it in my experiences.
But you're no pushover. You're no patsy. I know from watching you here. It's not JUST asking a question, it's asking the RIGHT question. Granted, you don't ask on a first date "Ok, so we're committed, and we're in this for the long haul, right?" But after some time, there is the opportunity to ask thoughtful, deeper questions. I know for me, with my wife, it was a couple weeks or so (I'm guessing) and we were talking about exes and I made a comment about "auditioning for the job of [boyfriend/significant other]" as a way to put out there that I understand that things have to progress, but to communicate my intention. Funny thing, a couple weeks later I got a text, out of the blue, saying "BTW, You're hired". It was our "language" so to speak. Personally, I would have no problem asking something along the lines of "So, here's what I'm hearing... blah, blah, blah... is that what you're saying?" Or if it's your style, make a joke out of it: "Hey, I only have three more invites on my card; if you're really interested, I'm going to have to recharge the card if I'm going to keep asking you out" (yeah, I know, that's stupid, but I'm spitballing).
EDIT: I just read the rest of the exchange. Honestly, and with respect, I think Cram is right. You're kind of looking at this only through the "Prog Snob" lenses. What about looking at it from her perspective? Maybe she was as honest with you as she can be? Maybe she's scared - or feels it's disrespectful - to tell you "yeah, I really like you but I'm sort of in limbo with this other guy" (the target of the Facebook post). I say this nicely, and not to you directly Prog Snob, but it's a little arrogant to think that these women are only talking to you.
To me, you're only a lap dog if you feel like a lap dog.