Former Minnesota Gov. Tim Pawlenty remains little-known beyond his home state, but he has begun to line up wealthy donors, a critical constituency. Even as he draws low single-digit support in early polls, Mr. Pawlenty has amassed a substantial roster of well-connected GOP donors and fund-raisers in his quest for the Republican presidential nomination. Their preference for Mr. Pawlenty could pose a challenge to his GOP rival, Mitt Romney, the former Massachusetts governor who has used experience as a 2008 candidate and background as a private-equity investor to build what is widely regarded as the largest network of high-impact fund-raisers...