VAIL, IOWA: Republican presidential hopeful Vivek Ramaswamy was more than 40 minutes into a town hall in rural Iowa when a woman in the crowd posed a pointed question. Or perhaps it was a suggestion.“I know you want to be president," she said. "But would you consider being Trump’s vice president?” The query drew light laughter from attendees and a lengthy response from Ramaswamy. (The short answer: No.)It also highlighted the central challenge facing the wealthy entrepreneur, who has risen from little-known newcomer to as high as third...