Perhaps you say a bad joke or you make a really awkward noise, and everybody suddenly stares at you?
This would be an awkward silence.
An awkward silence is an uncomfortable pause in a conversation or presentation. The unpleasant nature of such silences is associated with feelings of anxiety as the participants feel pressure to speak but are unsure of what to say next.
You could say that the room fell flat
If a joke, idea, or suggestion falls flat, it does not have the intended effect:
While it is primarily used to describe what was said, it can also be used to describe the room the statement was made in.
Alternatively, you could say that there was a deafening silence
A noteworthy silence, or absence of response, especially one signifying disapproval or lack of enthusiasm.
The suggestion that they work through the holidays met with deafening silence.
Hopefully a useful contribution, though maybe not your preferred answer:
faux-pas - a slip or blunder in etiquette, manners, or conduct; an embarrassing social blunder or indiscretion.
This does not necessarily imply everyone stops talking and stares, though. Faux-pas describes the "really bad joke or awkward noise."
The word conversation-ender describes both the awkward statement and the pause in conversation that follows. I didn't find any better authoritative source than Urban Dictionary, but a Google search shows it is fairly commonly used.
A word, phrase or emotion that abruptly and awkwardly ends a conversation between two or more people. [spelling corrected]
Describing unwanted silence and inactivity. Often used of a situation when one makes a statement that is ignored or ill-received from one’s audience. Gives the impression that a tumbleweed has passed through the room, as the resultant silence is likened to that of a desolate desert.