The poll also showed President Obama in a weak position in a state he narrowly lost in 2008. Missouri voters disapprove of the job he's doing by a 17-point margin.
Brunner is the front-runner for nomination, though not by a wide margin. He leads Steelman by 33 to 27 percent, with Akin clocking in at 17 percent support, according to the poll. Brunner has spent millions of his own money on the race so far, though Steelman has a strong political base in southwestern Missouri.
The poll of 625 likely voters, with an oversample of 400 likely GOP voters for the primary ballot test, was conducted from July 23 through 25. The overall poll has a plus or minus 4 percent margin of error, and the primary poll's margin of error is plus or minus 5 percent.