Seriously, I doubt it would even take that long. We get used to shit so quickly, and the news cycles have to keep feeding us new things, the only way we’d keep talking about the aliens if they kept doing new and interesting things. I’d be willing to bet a year later there would be some people who straight up forgot about it. “Oh yeah, aliens! Are they gonna, like, visit at some point or just keep exchanging calls with the Whitehouse?”
Yeah, I think there’d be the initial shock of it, but we’ve been pretty well primed as a society for the idea that, yes, life probably exists and it may already be here. So if it turned out they were just communicating with governments, it’d be like, “Oh, so they’re not even here? Huh, that’s… cool… I guess.” Communications would likely only ever come in every few years, so it’d more just be a matter of us having received a signal from intelligent life. Still be cool though, but shrugs would be the general response.
I don’t think many would disagree with that.