From quite a long way away.
Reverse-engineering this story from the Big City Newspaper, it's clear that the chief characteristics of "Prominent" Republicans are A) their complete lack of positions of power within the actual Republican party itself, B) a long absence from holding any elected office of any kind and C) an almost impervious cloak of media invisibly -- sort of like what Newt Gingrich would be if he made drastically fewer appearances on "Meet the Gregory" and if everyone in the Party of Personal Responsibility agreed to ignore him.
#1 The Huntsman
Charles P. Pierce has a helpful field guide here:
Seriously, is there one person on that list of serious influence in the Republican party, and it's not Huntsman, god knows, who is a person of serious influence only in the Republican party that exists in the heads of the people in various green rooms. Bill Weld, god love him, has been out of public life since 1996 and Jane Swift wasn't a "well-known" Republican in Massachusetts even when she was governor. Christine Todd Whitman is an influential Republican? Since when? You might as well be talking about William Seward.