U.S. Senator Thad Cochran prepares to cast an absentee ballot in the Republican primary runoff, at the Lafayette County Courthouse in Oxford, Miss. on Saturday, June 21, 2014. Cochran is being challenged by state representative Chris McDaniel. The runoff election is set for Tuesday, June 24, 2014. (AP Photo/Oxford Eagle, Don Whitten)

(Don Whitten)

JACKSON, Mississippi -- Mississippi election officials reported heavy absentee voting leading into Tuesday's Republican primary runoff for U.S. Senate, an indication of high interest in the intensely fought race between six-term Sen. Thad Cochran and tea party-backed challenger, state Sen. Chris McDaniel.

The candidates' campaigns and independent groups have spent millions of dollars on a steady flow of TV ads.

Groups that advocate limited government, such as Club for Growth and FreedomWorks, are backing McDaniel and see the Mississippi race as their best chance to unseat a long-serving Republican senator this year. Cochran, a former Appropriations Committee chairman, is campaigning on the slogan "more for Mississippi" and talking about federal money he has brought the state for disaster relief, agriculture, research and military bases.

Both candidates campaigned in the northern part of the state Saturday and are scheduled to head south Sunday.

"You still hold in you the potential to fight, the potential to stand your ground," McDaniel, 41, said Saturday at a Tea Party Express rally in Tupelo. "You believe what the founders believed, that self-government is inherited, it's yours for life, that the Constitution matters, that we're resilient individualists that can fight for ourselves. We don't need a government a thousand miles away to tell us what to do."

Cochran voted by absentee ballot Saturday morning in Oxford and spoke to potential voters in in Batesville, Vardaman, Amory, Aberdeen and Tupelo. He was joined at some stops by Mississippi's other Republican U.S. senator, Roger Wicker. Before heading to a four-county fish fry in Corinth, Cochran said he is trying to appeal to a broad cross-section of voters because he believes he would be helped by a big turnout Tuesday.

"I think we're going to have opportunities to influence spending decisions...to keep the government moving toward more savings, more jobs and a higher standard of living. Those are the benefits that flow from that," Cochran, 76, told The Associated Press.

With 318,902 votes cast in a three-person race June 3, McDaniel received 1,418 votes more than Cochran, but neither had the majority required to win.

Noon Saturday was the deadline for in-person absentee voting for the runoff and mail-in absentee ballots must be returned by 5 p.m. Monday.

Several Republican counties reported an increase in absentee voting for the runoff compared to the June 3 primary -- a reverse of the typical drop-off between a primary and a runoff. Among those reporting an increase are DeSoto and Lee counties in the north, Madison and Rankin in central Mississippi and Jackson County on the coast.

Absentee voting is also heavy near the candidates' homes. Cochran lives in Lafayette County and McDaniel in Jones County.

"I've been here for 27 years and usually, these little elections, we just breeze right through them. We working our buns off now," Lafayette County Circuit Clerk Baretta Mosely said Saturday.

Glance at absentee voting in some Mississippi counties

JACKSON, Miss. (AP) -- Here's a glance at absentee voting levels in some Mississippi counties that are important to the Republican primary runoff for U.S. Senate, according to elections officials surveyed Saturday by The Associated Press:

-- DeSoto County, just south of Memphis, Tennessee, is Mississippi's fastest growing and among the most Republican-dominated counties. Circuit Clerk Dale Thompson said she expects at least 700 absentee ballots to be filed. That's up from slightly more than 400 absentee ballots that were cast for Republicans and Democrats, combined, before the June 3 primaries.

-- Harrison County issued more than 850 absentee ballots for the runoff, said Connie Ladner, deputy circuit clerk. That compares to about 1,100 before the first primary, which also included a high-profile U.S. House primary.

-- Hinds County has two courthouses. The one in Jackson has issued roughly 300 to 350 absentee ballots for the runoff, said Loretta Wells, deputy circuit clerk. A call to the Raymond courthouse was not answered shortly after noon Saturday. Wells said about 730 absentee ballots were issued for the entire county for the June 3 primaries, a figure that includes Republican and Democratic voters.

-- Jackson County issued more absentee ballots for the runoff than for the June 3 primaries, said Jackie Fortner, chief deputy circuit clerk. She said 518 had been issued for the runoff; a number for the primary was not immediately available Saturday.

-- Jones County, the home of challenger Chris McDaniel, issued about 850 absentee ballots for the GOP Senate runoff, said deputy circuit clerks in the county's courthouses in Ellisville and Laurel. That's up from roughly 660 for both parties' June 3 primaries.

-- Lafayette County, the home of incumbent Thad Cochran, issued more than 500 absentee ballots for the runoff, said Circuit Clerk Baretta Mosely. That's up from 354 for Democrats and Republicans combined before the June 3 primaries.

-- Lee County absentee voting is "a lot heavier than it was in the first primary," said Carol Horton, deputy circuit clerk. She said about 570 absentee ballots had been issued for the runoff. A number for the first primary was not immediately available Saturday.

-- Madison County issued about 1,000 absentee ballots for the runoff, compared to about 300 for the primary, said Circuit Clerk Lee Westbrook.

-- Rankin County issued more than 1,000 absentee ballots for the runoff, compared to a little over 700 for the primary, said Becky Pouncey, deputy circuit clerk.