I've been to that chapel twice. The staircase is something to see, but in and of itself, it's not manifestly miraculous. But who am I to say? It is certainly within the power of Almighty God, to send someone who would be capable --- naturally or supernaturally --- of building something like that, with the knowledge of physics it would have taken to do it. I have to doubt that anyone in 19th-century Santa Fe had that kind of knowledge.
If you've never been, do take the trip. Don't miss Chimayo, it's about an hour out of Santa Fe. The Inn at Santa Fe (8376 Cerrillos Road, just off I-25) is clean, economical, and has great views --- in Santa Fe, there aren't really any other kinds of views.