Even Republicans who have embraced Mrs. Fiorina in recent days — and expect her to earn a place in the top tier at the next debate on Sept. 16 — privately concur she is an imperfect candidate. A single previous campaign, for the United States Senate from California in 2010, ended in a nearly double-digit defeat. Her corporate resume is notable for her firing as chief executive of HP — a humiliation that Mrs. Fiorina tries to explain as the price of bold leadership.

She is already being pressed about the 30,000 layoffs at HP under her watch. Similar criticism wounded Mitt Romney, the 2012 Republican nominee, whose career at Bain — and its deals that resulted in layoffs — exposed him to Democratic attacks that he did not care about the middle class.

Asked about the layoffs while she was chief executive, Mrs. Fiorina said she would take a similar approach to the federal government. “I do think there are a lot of people who think it would be a good thing if the federal government were more effective, more efficient and a lot less bloated,” she said.

It is unclear how much her message will resonate with women. Mrs. Fiorina once said her experience proved the glass ceiling was obsolete, and she has defined feminism as “a left-leaning political ideology” that pits “women against men” and is “used as a political weapon to win elections.”