Derek Jeter, while a great overall player and deserving future Hall of Famer, rates as a below average defensive shortstop by just about every defensive rating system that has been devised. He does not have good range on groundballs, but some say that he partially makes up for this by being great on relay throws (which I won't argue with) and catching popups.
Statistical evidence is hard to come by on popups, but I thought I'd give it a try. I need to look at it on a team level, since popups are almost always balls that can be caught by more than one fielder. I look at every popup, as coded by retrosheet, that is fielded by the shortstop or an adjacent fielder (3B, 2B, LF, CF). If the catcher, 1st baseman, or rightfielder catches a popup I'm going to assume that the shortstop has nothing to do with it. I get counts of how many were caught by this group of fielders, how many fell in for hits, and how many the shortstop handled.
For 2003-2007, all but 2.63% of popups to this fielding group were caught. Shortstops typically handle 35% of these.
Derek Jeter catches 36%, pretty much average. Out of 1176 popups, 36 fell in for bloops while Jeter was the shortstop, which is 5 below average. I would not use this to further knock Jeter's defense for two reasons: 1) Its only 1 extra popup per season, hardly a big deal and 2) The blame for these bloops is not all Jeter's, some goes to his teammates.
The shortstops who allow the fewest extra bloops were Bartlett, Lugo, and Aurilia (+6 each). The worst are Hanley Ramirez (-11), Troy Tulowitzki (-7) and Tony Pena (-7). Adam Everett (-5) was tied with Jeter.
These low rankings could be a product of luck, or bad fielding teammates, or maybe the shortstop is just not good at this area of the game. Statistical analysis can show there might be a problem, it would take some observation to confirm it. The bottom 3 are all 1st and second year players, it could be an experience thing.
Tulo caught 49% of the popups among his adjacent fielders, so it looks like he's a take charge guy. Perhaps his other fielders are backing off too soon and thinking he'll catch it? Lugo (42%) and our old friend Orlando Cabrera (41%, +1) try to get as many as possible too.
At the other end, Tejada, Clayton, Felipe Lopez, Renteria, and Jack Wilson only catch 31% of the popups. They are quite comfortable letting someone else handle it. For Tejada, it works out just fine, when he was on the field his team was +4 on popups.
Play by play defensive systems usually ignore popups. That its not a big deal as far as runs saved seems to be a safe assumption. In just a few cases a popup rating could have a significant impact on a defender (Tulo, Hanley) but once you figure out how to divide the credit/blame among all the fielders who could have made a play and account for regression to the mean, the impact will be minimal even for these guys.