The poll, conducted by North Star Opinion Research, pegs Alexander's job approval among Republican primary voters at 69 percent, with 24 percent disapproving of the job he's done.

And among a wide swath of the Republican primary electorate, including what the memo refers to as "key subgroups" within the party, a majority of voters approve of Alexander's job approval.

Seventy-four percent of strong Republicans, 70 percent of Evangelical Christians and more than half of very conservative voters and Tea Party supporters approve of the job he's done.

He also leads every announced and potential primary opponent by 39 points or more. Thus far only second-time candidate Brenda Lenard and state Rep. Joe Carr have entered the race, neither of whom are likely to pick up steam; Knox County Mayor Tim Burchett and conservative activist Kevin Kookegey have expressed interest in the GOP primary.

Alexander polled matchups with all four.

While the poll is good news for Alexander, it's also an indication that he's taking the potential for a strong primary challenge seriously.

That concern is likely sparked in part by the interest conservative groups have already begun to show in the race.

Last week, the Senate Conservatives Fund launched a radio ad targeting Alexander for his refusal to sign onto a conservative-backed pledge to shut down the government by voting against any budget that includes funding for ObamaCare.

Alexander has long been an outspoken critic of the law. But in a move that revealed just how wary he is indeed of a potential primary challenge, Alexander answered the SCF ad with one of his own, touting his opposition to the law.

The survey was conducted among 600 likely Tennessee Republican primary voters from Aug. 19-22.