When conservative activist and former presidential candidate Gary Bauer scans the potential 2012 Republican field, not much excites him. "All the obvious frontline names have all the usual pluses and minuses," Mr. Bauer says.

But in considering one candidate, Mr. Bauer sees only qualities that he likes. Indiana Rep. Mike Pence is a military and fiscal hawk who frequently plugs his Christian credentials. To some, he's the potential candidate best able to unite two wings of the Republican Party—its fiscal conservatives and social...