Sen. Thad CochranThad CochranOvernight Defense: FBI chief confirms Trump campaign, Russia probe | Senators push for Afghan visas | Problems persist at veterans' suicide hotline Senators ask to include visas for Afghans in spending bill Shutdown politics return to the Senate MORE (R-Miss.) is starting off in a weak position against a tough Tea Party challenger, according to a new poll conducted for the conservative online magazine Human Events.

Cochran is tied with Tea Party-backed Chris McDaniel at 40 percent among GOP voters who've voted in a recent Republican primary, not a good spot to be in for the long-term incumbent.

The senior member of the Appropriations Committee appears to be the senator most vulnerable to a primary challenge, and McDaniel has won the endorsements of a number of big-spending conservative groups including the Club for Growth.

The poll of 691 regular Republican primary voters was conducted Dec. 13 by Gravis Marketing, a Florida-based firm whose results tended to skew Republican in the 2012 election cycle.