The Vanderbilt University poll shows 53 percent of Tennesseeans polled approve of the job he's doing as senator, a figure largely unchanged since November 2011, according to the polling memo.

Alexander's greatest concern hasn't been with a potential Democratic challenger, however, as Tennesseeans feel largely negative about President Obama, with only 40 percent of them approving of the job he's doing.

The incumbent has, however, long been considered vulnerable to a primary challenge, as conservatives are dissatisfied with his vote for the financial bailout and his bottom-10 score from the Conservative Club for Growth last session.

No conservative challenger has yet emerged, but World Wrestling Entertainment star Glenn Jacobs, known by his stage name "Kane," has reportedly expressed interest in the race.

But Alexander maintains his highest approval in this new poll among Tea Party members, with 62 percent of them viewing him favorably. That level of support from the far-right of the party would make it difficult for any potential primary challenger to mount a credible campaign against him.

He is thought of positively by a majority of Democrats, independents and Republicans, as well.

The Vanderbilt University poll was conducted among 813 registered voters from May 6-13, and has a margin of error of plus or minus four percentage points.