A day after losing Mississippi and Alabama to Rick Santorum, Mitt Romney took his campaign to a state where he had no public schedule, no time carved out to mingle with voters, and no rallies or town halls. While Mr. Santorum and Newt Gingrich hunted for votes in Puerto Rico and Illinois, Mr. Romney traveled to New York City to raise money and reassure top Republican donors — a constituency that favors his candidacy, and one perhaps most rattled by his inability to win the confidence of the party’s conservative base. Mr. Romney has raised more than $63 million, twice...