His candidacy all but dismissed just days ago, Rick Santorum won the Minnesota caucuses and a nonbinding primary in Missouri on Tuesday, raising fresh questions about Mitt Romney’s ability to corral conservative support.

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Mitt Romney campaigning Tuesday in Loveland, Colo. Early results had him far behind Rick Santorum in the state's caucuses. More Photos »

Mr. Santorum was also running strongly in Colorado, a state Mr. Romney captured four years before. With a quarter of the vote counted by...