WASHINGTON — At 23, Elizabeth Pipko has branded herself on social media as a onetime figure skater, a part-time poet and a former Trump campaign aide, an Instagramista whose feed spotlights her Mar-a-Lago wedding and racy swimsuit and lingerie modeling shots.

But when President Trump latched onto Ms. Pipko’s concept of a “Jexodus” — a fledgling, and some would say crass, effort by Republicans to woo Jews away from the Democratic Party — even Democratic leaders found themselves defensively responding to a young woman they did not know existed a month ago.

The rise of Ms. Pipko and the notion of a Jexodus — there is no evidence that any such thing is occurring — is an object lesson in how an idea can migrate from a no-name messenger to the broad body politic, through the organ of Fox News and the megaphone of the president’s Twitter account.