Could Tesla have REALLY shaken a building with a little oscillator?

I came across this story while reading about Nikola Tesla ground-power scheme. Supposedly, he created a little oscillator that could be plugged into the ground, tuned to the right (resonant) frequency, and clamped on to an entire building to shake it down. Could this work? Tesla often exaggerated or lied about his inventions to bring in investors (and therefore became a "New Age Cult Hero"). Yet resonant oscillation can be really powerful — as seen in the oft-mentioned Millenium Bridge debacle, or in the wine-glass-breaking-scream trick, or a person on a swing set (Side note: I knew someone who said that he once went the full circle!). However, it can only work if more energy is put in than is lost with each cycle. Would the energy lost from the oscillations of the structure be more than covered by Tesla’s little vibrator?

Also, his idea to "break apart the Earth" with resonance couldn’t work… could it?