IMO - Jeter will not get 3000 hits.
Players who I think have a shot (other than the obvious Palmeiro):
Pujols - 787 after 4 seasons (24 years old)
A-Rod - 1707 after 11 seasons (28 years old)
Juan Pierre - 859 after 5 seasons (26 years old)
However, its really still to early to tell with these guys. You have to play a LONG time to reach 3000.
I'm curious as to why you don't believe he will get to 3,000 hits. He will only be 31 in a few days and should easily finish with over 1,900 hits this year.His 162 game average throughout his career is 206 hits. Barring injury, that will get him to 3,000 before his 37th birthday. If Jeter is not spectacular, he is extremely consistent. If he cuts down on the strikeouts and stays healthy into his early 40's, he could actually attain 4,000 hits. I'm not saying it will happen, but it certainly could.
Jeter has played 10 years, 8 of them 'full' seasons. In the 8 seasons he played he avg'd 196 hits. If he maintained that avg for the next 4 years (including this season) that would put him at 2518 at age 34 (35 in June).Omar Vizquel is the only shortstop that I can think of that is still a starter at that age (he's 37), and that is because he's one of the best fielding shortstops in baseball history.
Jeter IMO is an above avg fielding shortstop right now, but that's it. 4 years from now will he still be able to cut it at short? A-Rod will be 32 - going on 33 at that point so I think its unlikely he's moved on or vacated the 3B position. So that's one issue.
The second issue is that we've assumed he'll maintain that 196 hit average. At this point he doesn't seem to be slowing down, but he will eventually, its just a matter of when.
Another negative is he doesn't have a ton of power. A lot of the 3000 club are able to maintain their careers because even if the batting avg suffers, they still have some pop. This won't be the case for Jeter, he'll need to continue to stay a .300 hitter throughout his career. (which, in retrospect, severely damages Juan Pierre's chances)
Finally, so at 34 going on 35 he still needs 482 hits. Which means he'd have to at least play 3 full seasons or play part time in several more seasons. Which means he'd have to be a full time player until age 38 or a part-timer into his 40s. Jeter is already a very rich man, do you think he'll still want to be playing at that age?
Its just my opinion, but I'd be surprised if he makes it. Of course its certainly not out of the question, but personally I'd give him a 10% chance.