So 2..a6 being our main move, lets look at why 3.d4 is not such a good move:
Let's compare our first line to this position in the Sveshnikov..be sure to read the annontations.
Now, this is all good fun if white makes the mistake of bringing his knight back. However most players above 1600 are knowledgable enough to know the Nb5 is the best move. Nb5 enters the mainlines and white can pose black some problems.
Now that we understand this, lets take a look at what happens after 3.d4?! in our O'Kelly variation
There is one more important variation to know, this time it is an improved version for the O'kelly!
So this is all fine and dandy, but white obviously has better moves.
The mainline in the O'kelly sicilian is 3.c3! The idea is to transpose into a sicilian alapin with nf3 and a6 inserted. Nf3 is usually played anyway, but a6 isnt very useful which is why this plays to whites advantage.
However..if we think for a moment, most alapin players will play c3 on the second move rather than the third. If you do come across the person who knows the mainline, its unlikely they will be well versed in alapin positions if they usually play open sicilian against everything else, so you still have the advantage of being more accustomed to the resulting positions.
Before we look at the Mainline Id like to quickly show you my recommended moves against the Alapin and the Smith morra gambit:
Now with this out of the way I recommend you play ..nf6 against the mainline O'kelly. The recommended move by theory is ..d5, which is the alternate mainline in the alapin. However this doesnt have the abaility to be used against BOTH the alapin and SMG, and learning a second line for the rare occasion you face O'kelly mainline isnt practical.
So I recommend you play 3..nf6 after: 1.e4 c5 2.nf3 a6 3.c3
as said a6 isnt as helpful as nf3 but you should have a playable position. Also, as youre lagging in development I find this line is better to keep the position closed than the ..d5 lines anyway.
Now, there is actually a way for white to backdoor into an open sicilian, in which case you would need to play the Najdorf or a kan/schevenigen/taimanov. and thats with 3.nc3
Other than this you will still need to choose a setup against the Grand Prix, early maroczy 2.c4 or 3.c4 and closed which you prefer, also a setup against early Bc4 lines which are often played would be beneficial to have ready.
Personally i play 3..e6 against all of them followed by a quick d5 or queenside b5 expansion. However this fits my repertoire with Kan (rather than najdorf) very well, perhaps you may try to find some variations which better suit your najdorf structure.