Only Hall of Fame running back Emmitt Smith has more consecutive games with 14. McCaffrey could tie that record this weekend against Smith's former team, the Dallas Cowboys.
While Rice expressed genuine delight for McCaffrey, he did share the following tidbit during a Thursday morning interview on 95.7 The Game.
"I'm behind [the record being broken] 100 percent," Rice said on "The Morning Roast" show. "I give him credit for that. But I might only get five touches in a game. I [did] not get 27 touches or more. And if I had gotten that, I probably would have doubled all my yardage and stuff."
Rice emphasized, "But I'm behind him 100 percent, and I was glad to see him get that done."
Like fans, the Hall of Fame receiver is in awe of what McCaffrey is accomplishing on the football field.
"CMC is getting it done, man," Rice said, noting that he is concerned with the workload the 49ers are placing on McCaffrey's shoulders. "... But whenever he touches the football, he's electrifying. He's amazing. He knows how to get into the end zone."
McCaffrey already has one season with over 1,000 yards rushing and receiving, an accomplishment first achieved by should-be-in-the-Hall-of-Fame running back Roger Craig. Rice shared a locker room with Craig for numerous seasons. Can he draw parallels between McCaffrey and Craig?
"I see shades, but I also see a guy that is faster with him running the football than with him coming out of the backfield, catching the ball," Rice shared. "He's an unbelievable weapon, and you know that he's going to put points on the board. And we always base the offense around the running game. If you get that running game going, it's going to open up everything else.
"I think Dallas has got a big challenge coming in because, with that defensive line, that defense, they got to be aware that this guy can catch the ball out of the backfield, but he's also very productive at running the football."
You can listen to the entire conversation with Rice below.
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