The closest anyone has come was Reggie Brooks in 1992. He was a single called-back run vs. U.S.C. from tying the record. And for him to do so, it took numerous 20-plus yard runs (including an 80-yarder) off an option pitch where the defense was accounting for Bettis on the initial read and Mirer on the keeper, as well as the fact that the primary short-yardage recipients of the ball were frequently Jerome Bettis or Jeff Burris.
We rarely run the ball out of two-back formations and never do so out of three-back formations, so Price gets a fair share of short-yardage carries, especially since he's pretty darn good at it.