I have to run a very long footage in CS6 for stabilizing only and not working on anything else. What can I do to put forth more RAM and CPU into this " background " function?
Nothing. The plug-in is designed to work in the background and it only utilizes one main core and accesses only the memory it needs to look at a frame.
There's only so much data in a problem. You can't devote 16 cores and 128GB of ram to a problem that only contains 2 kilobytes (an HD frame is about 2K) of data. When footage is stabilized the pixels in a single frame are analyzed to try and find some areas of high contrast. That's just not very much data. Once the significant detail in the frame is defined it is compared with the detail in the preceding and following frame to find some matching areas. Without rewriting the routine to load every frame in the file into memory and then simultaneously analyze as many of them as will fit in system the system you're simply not going to be able devote all system resources to solving the problem.
The warp stabilizer will also not work very well on very long shots with a lot of movement. Neither does the 3D camera tracker. At some point the analysis will either fail or the stabilization will jump from one solution to another.
An extrordinary long shot in a movie would be something that lasts over a minute. Make sure you're going to need the entire shot you are trying to stabilize by cutting it into a project first and then stabilizing only the portion you need plus a few frames on the head and tail. It's a more efficient way of film making.
What Rick said - you can't enforce what mathematically and physically is impossible. The warp stabilizer requires temporal coherence and thus operates strictly linear one step at a time. Not saying that AE couldn't use multiple threads to mdo the hard math, but loading the frames would still be linear...