"The more the tea party complains about how black voters vote for Republicans, I think they look racist and stupid," said John Feehery, a GOP consultant in Washington. "We're trying to get black voters. Now that one of our candidates got black voters, we should be happy about it."
Nearly 377,000 people voted in Tuesday's runoff in Mississippi, and Cochran received nearly 6,800 votes more than tea party-backed McDaniel.
"There is something a bit strange, there is something a bit unusual, about a Republican primary that's decided by liberal Democrats," McDaniel said to a roar from supporters on election night in Hattiesburg. On Wednesday, he still refused to concede and vowed instead to investigate vote patterns for "irregularities."
Turnout was up significantly from a three-person primary on June 3, when McDaniel had finished about 1,400 votes ahead of Cochran but nobody received a majority to win.
Importantly, turnout in Mississippi's majority-black counties grew by 43 percent from June 3 to the runoff, while in majority-white counties, it grew 17 percent.
When reporters in Washington asked Sen. Roger Wicker, R-Miss., if Cochran's appeal to Democratic voters might have a negative impact on the GOP, Wicker responded with a laugh.
"Broadening the base of the party? Asking more Mississippians to participate in the ballot that's going to determine the next senator? No, I don't think there's anything wrong with that," he said.
Cochran, a former Appropriations Committee chairman, made no secret of trying to draw support from any Mississippian legally allowed to vote. Mississippi does not register voters by party. Under state law, the only voters barred from participating in the Republican runoff were those who cast a ballot in the June 3 Democratic primary.
With an increase in turnout, Cochran won with nearly 52 percent of the vote.
It was an improbable achievement of a key but elusive goal for the GOP: find a way to survive in a nation where growing numbers of African-Americans and other minority voters overwhelmingly cast ballots for Democrats. Birth rates among whites are shrinking in the U.S., while racial and ethnic minorities are expected to make up a majority of Americans within about 30 years.
Exit polls conducted for The Associated Press and the networks showed that only about 6 percent of black voters identified themselves as GOP voters in 2004, and 4 percent did so in 2008 and 2012.
Republicans in Washington distanced themselves from a candidate's complaint about drawing black voters for a white candidate in racially polarized Mississippi.
South Carolina Sen. Lindsey Graham, who recently defeated several tea party challengers in a Republican primary, told reporters: "If Thad did get a bump from African-American participation in the Republican primary, that's probably the best news I've heard in a long time."