This a tremendous read by a NFL Draft nut Eric Stoner (@ECStoner on Twitter). It basically supports what I've been trying to say (we need to take a QB round 1).
The summary is he groups quarterbacks into 4 tiers. The top 2 tiers pretty much consist of the best quarterbacks in the league. Tier 3 he describes as "good enough to not get replaced" and tier 4 is the Brady Quinn's of the world.
Of the 13 QBs in the top 2 tiers, 11 of them were first round draft picks. The only two were Drew Brees (1st pick in the 2nd round) and Matt Schaub (3rd round).
The Chiefs, in order to maximize their chances of getting a QBOTF (a tier1/tier2 guy) need to take a QB in the first round.