Established Republican leaders, from Senate GOP leader Mitch McConnell to former Mississippi governor and Republican Party chairman Haley Barbour, side with Cochran as a proven general election powerhouse who will become chair of the powerful Appropriations Committee if Republicans recapture the Senate. They warn that McDaniel, beset by several controversies over his past statements and the actions of his supporters, might even lose the seat and thus jeopardize prospects for Republican control.
Staunchly conservative outside groups, from various tea party organizations to the Club for Growth, back McDaniel as a needed challenge to Washington's go-along, get-along culture. They seek a more confrontational Republican Party, shrugging off warnings that the GOP must move to the center to broaden its appeal and compete in presidential elections.
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The battle carries high stakes for economic policy. The Republican Party's more conservative wing opposes reauthorization of the Export-Import Bank, denouncing the help it provides businesses in international deals as "crony capitalism." It opposes comprehensive immigration reform, a top priority for the U.S. Chamber of Commerce and other business groups. It opposes new taxes to finance an extension of the federal highway program, which is running short of funds. It has been willing to risk government shutdowns and defaulting on U.S. debt in order to force through spending cuts that Congress otherwise would not pass.
McDaniel and Cochran met initially in a June 3 primary contest. McDaniel finished slightly ahead—but just short of the 50 percent needed for victory due to the small number of votes who went to a third candidate. Tuesday's contest pits only the two candidates.
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Political observers generally expect McDaniel to win, since his supporters have appeared more motivated, and runoff turnout usually is low. But Cochran and the skilled political operatives supporting him have devoted considerable energy to try to expand the electorate by turning out African-Americans and other Democratic-leaning voters who have backed him in past general elections.
Mississippi's election rules allow any voter to cast a ballot in the runoff except for those who voted in the Democratic primary on June 3. That primary nominated former Rep. Travis Childers as the Democratic standard-bearer. Democratic leaders acknowledge that Childers would have no chance of beating Cochran, but insist he'd have an outside chance of winning in this red state if Republicans nominate McDaniel.
—By CNBC's John Harwood.