If the Kansas City Chiefs are going to find a quarterback in the NFL Draft, it's not likely going to be in the first round. Contrary to what many Chiefs fans would love to see (i.e. Scott Pioli trading up to grab Robert Griffin III), the Chiefs will likely address other positions before getting to any developmental quarterback possibilities. However, Kirk Cousins in the third round would be an interesting grab for a team with a hole at back-up quarterback.
Ricky Stanzi was the choice last year, but he didn't play a single down during the regular season despite Tyler Palko starting four games (and costing Todd Haley his job). While no official roster decisions have been made, it's hard to see how Palko could come back as the primary back-up for another year in Kansas City. Thus it's likely that the Chiefs will either sign another veteran or draft a promising player they like.
As for Cousins' ability, the Michigan State quarterback had 3,316 passing yards this year to go with 25 touchdowns and 10 interceptions. Wes Bunting likes him as an NFL starter if he can clear some mental hurdles. He writes, "A solid athlete who isn't overly impressive physically, but he has enough to make it in the NFL. Needs to take that next step in his understanding of the offense this year and cut down on the mental errors. However, he's a good kid, a hard worker and has some real similar qualities to some of the senior quarterbacks who came off the board this year (Ponder/Dalton). Nevertheless, his struggles with pressure could hold him back from ever becoming an NFL starter."