Longtime Sen. Thad Cochran, R-Miss., one of the Senate’s most senior members, was in the fight of his life Tuesday as challenger Chris McDaniel pressed him in the state’s Republican primary.

With 95 percent of the vote in, Cochran, 76, had 49.0 percent and McDaniel, 41, a state senator, had 49.4 percent, according to the AP. Thomas Carey had 1.6 percent. Under Mississippi law, a candidate must top 50 percent to avoid a runoff. The winner will face former Rep. Travis Childers, who easily won the Democratic nomination.

Primaries were held in seven other states Tuesday, with few surprises. In South Dakota, former Gov. Mike Rounds won the Republican nomination for the seat being vacated by Sen. Tim Johnson, a Democrat. He will face Democrat Rick Weiland. The seat is a prime GOP pickup opportunity.

Republican Govs. Robert Bentley of Alabama, Dennis Daugaard of South Dakota, Terry Branstad of Iowa and Susana Martinez of New Mexico all won renomination. Gov. Jerry Brown was practically unopposed on the Democratic side in California.

Cochran was first elected to the Senate in 1978, when McDaniel was five years old. He is the ranking Republican on the Agriculture Committee and former chairman of both that committee and Appropriations.

If McDaniel pulls off an upset win, one of the nation’s most conservative states could suddenly be put into play in a very tough year for Democrats to hold control of the Senate. Mississippi has not elected a Democratic U.S. senator since 1982.

The Mississippi Senate race is "talked about as a Tea Party race, but it's more about the conventional challenge of an incumbent," John Bruce, an associate professor and chairman of the political science department at the University of Mississippi, told USA Today. "The Deep South has a long history of liking incumbents and we tend to like them until they die. But the magic of incumbency has died a little."

Early on in the primary, McDaniel was dogged by associations with neo-Confederates and secessionists, as Talking Points Memo noted. Even the Mississippi GOP chairman said McDaniel should treat questions about his associations with white supremacists seriously. McDaniel had also received criticism for saying that he probably would have opposed legislation giving $10 billion in aid to Gulf Coast states hit by natural disasters.

Then a McDaniel supporter went to the nursing home of Cochran's bedridden wife, who reportedly suffers from dementia, to photograph her for an anti-Cochran video.  If McDaniel survives the primary, he could face more questions about the ongoing criminal investigation.

Democrats also would use McDaniel’s days on talk radio against him.

"There's a long history of radio talk show clips that will be evidence that he's out of the mainstream on many issues," Democratic pollster Brad Chism told TPM.

In November, the Democratic-leaning Public Policy Polling found that Childers and McDaniel were virtually in a dead heat: 41 percent for McDaniel and 38 percent for Childers. But against Cochran, Childers trailed by double digits, 50 percent to 33 percent.

Democratic pollster John Anzalone, whose polling firm will be doing work for Childers' Senate race, said he expected "a lot of Cochran supporters, politicos, funders … to flock to Travis Childers if McDaniel does this."

"I think there would be a stark contrast between me and state Sen. McDaniel," Childers said in an interview with Politico on Friday. Childers can be expected to portray him as a "far-right extremist."

Childers says he’s no liberal himself, and contrasts with other Democrats in that he considers marriage to be between a man and a woman, voted against Obamacare, and is against new restrictions on guns.