DES MOINES — After 11 Republican presidential contenders spoke to a huge gathering of Iowa party activists at the Lincoln Day Dinner this month, they moved to hospitality suites to greet people one on one.

Jeb Bush’s suite looked sparse, with a handful of visitors asking the former Florida governor for a photo. Rick Santorum said hello to a scattering of old supporters.

But the line to meet one candidate, Carly Fiorina, a former Silicon Valley executive whose name recognition is negligible among voters, snaked down the hallway. For more than an hour, Iowans filed into the suite for their chance to meet Ms. Fiorina.

Ms. Fiorina, a former chief executive at Hewlett-Packard with a flair for biting one-liners, had just delivered a speech that included references to God and a joke about former President Bill Clinton’s hormones. When a timekeeper cut off her microphone, indicating that she had used up her allotted 10 minutes, the audience broke out in catcalls and groans. The crowd wanted more Carly.