Edit: Now there's a chance he won't have surgery for now.
As Dave Cameron stated, the Yanks (nor any of the top American League East teams really) can ill afford to have their best player(s) miss significant time in such a clustered division. Cutting to the chase, what everyone wants to know is how much Alex Rodriguez missing time is going to hurt the Yankees.
Over the last three years A-Rod has averaged ~4.3 plate appearances per game -- adjust that upwards if you think the Yankees offense is extremely improved, otherwise it seems like a decent number to use here. At the same time he's averaged about 0.32 wRAA per game using that plate appearance average. Defensively Rodriguez has averaged basically 0 runs per game, -0.03 if you want to be precise.
All we need to know is how many games he'll be out, and how his replacement stacks up. Here's a look at what the Yanks are missing with a replacement level player stepping in:
Alex Rodriguez absence filled by Replacement Level Player
| Games | Offensive | Defensive | Replace | Total | Wins AR |
| 10 | 3.2 | -0.3 | 1.4 | 4.3 | 0.43 |
| 20 | 6.4 | -0.6 | 2.9 | 8.7 | 0.87 |
| 30 | 9.6 | -0.9 | 4.3 | 13 | 1.3 |
| 40 | 12.8 | -1.2 | 5.7 | 17.3 | 1.73 |
| 50 | 16 | -1.5 | 7.2 | 21.7 | 2.17 |
This is hardly a perfect analysis, but it seems like a decent ballpark figure. Remember, that's the amount of wins Rodriguez adds, so those numbers are actually negative for the Yankees outlook. Wilson Betemit is likely giggling in southside Chicago because Cody Ransom is apparently the Yankees back-up. Ransom isn't much better than a replacement level player, so bump off maybe a half of a run from those projected totals and you have the impact felt by A-Rod's hip.
Now obviously, the Yankees could always go out and trade for a third baseman or sign someone to fake third for a month, so this could always change. Now watch the Yankees go on a 30-10 rip without Rodriguez.