The moonshot nature of these candidacies, and the fervor for them regardless — the candidates, in both parties, have made the rounds on Fox News and become darlings of conservative media — underscores the fame and rancor that have surrounded Ms. Ocasio-Cortez.

The campaigns also highlight a broader strategy by the Republican Party: turning voters’ resentment toward Ms. Ocasio-Cortez into a conduit for the party’s other electoral goals. By encouraging attacks on Ms. Ocasio-Cortez, Republicans hope to inspire a trickle-down effect onto lower-profile, but much more vulnerable, Democrats…

But for the challengers, running — even with a near-guarantee of defeat — has few downsides. They can raise thousands off Ms. Ocasio-Cortez’s name alone; earn exposure for future campaigns; and bask in the attention, even if only for a short time.