CHICHESTER, N.H.—After punching her way onto the big stage, Carly Fiorina is poised to take on her party’s heavyweights in Wednesday’s Republican presidential primary debate, where she will come face-to-face with the candidate who found fault with her face.

Mrs. Fiorina distinguished herself in the first undercard debate with an acerbic wit and a strong command of foreign policy. The question now is whether she can stand out in a larger, more combative crowd of 11 candidates. At center stage will be Donald Trump, who derisively...