People are already doing similar things informally, see
this page for an example. Of course I do not recommend anyone doing what they discuss on that page. :evilgrin:
But publicly distributing interesting and well designed pamphlets, and putting pamphlets and other reading materials in the same drawer as the Gideon Bible in hotel rooms sound like excellent ideas.
What's needed for the hotel distribution is to mobilize a large group of secularists who, for business or other reasons, stay in US hotels often. Other people who travel only occasionally, maybe once a year for vacation, could also do it, but the regular travelers would be the mainstay of the effort.
I'm not sure how well a speaker like Ingersoll would do today. There's only a very small percentage of the population that would bother to go see any public speaker. What might be needed is someone who is also entertaining in other ways. One person comes to mind, although there may be others - Penn Gillette (of Penn and Teller). While I disagree with a lot of his politics, he is a staunch and outspoken secularist and he also puts on a very entertaining magic show. I once saw him, in the middle of a magic show, enthrall an audience with a lecture in which he said things like "most people accept the first explanation they hear for something and then never think about it again". He can definitely grab people's interest and attention. Of course, that's just an example and their may be better choices. An entertaining comedian, for example, might be very effective at mocking fundies while talking about the inaccuracies and inconsistencies in religious texts. Laughter might be effective at cutting through some people's willfull resistance to new ideas.
TV might actually be a possibility, at least on some cable channels. South Park, for example, regularly and openly mocks religion. They even did an episode that was basically a hostile expose on the history of Mormonism. The Comedy Channel in general tends to be quite irreverent in its programming.
It's possible that people might be more open to questioning then we realize. I think there are many many nominal Christians out there who go to church only on holidays and have accepted, with little thought or understanding, the overall teachings of their church (or at least what they
think those teaching are). They've simply had very little exposure to the idea of asking questions and thinking through the things they've been taught.