Is it even possible to set up a system in 12x12 room?

I think you can get a system together that will sound pretty good if you accept limitations in terms of bass response.  The biggest issue I have run into is not being able to get adequate space between the speakers (9' minimum is ideal) and distance from back wall. 

Many speakers have minimal issue in terms of near wall placement.  If you can be 8' away from speakers that are 9' apart and are 2' from the back wall...you should be in a good spot.  

My biggest concern is couch directly on back wall, I would think I need to pull it out into the room, am I wrong? Problem is there's not much room to pull couch into. I'm very glad to hear many have success in smaller than average rooms, I do feel better knowing that. This system was in bigger room and speakers disappeared. if I place myself near field will I hear music coming from speaker or will they disappear. When I place myself near field with this system in bigger room I hear the speaker, there is still imaging but not the same type of sound stage.

Paul,

I had to relocate my system into my daughters old bedroom which is 12x12x8. My speakers are placed about 3-1/2 ft from the front wall and 3 ft from the sides walls so the speakers are 6 ft apart. My sitting position is about 1-1/2 ft from the back wall and approximately 6-1/2 ft from each speaker. I installed wall to wall carpeting. 
I use GIK bass traps on the front corners and placed 2’x4’x4” panels at the side reflection points that also help with the bass. I placed 2 2’x4’x2” panels behind my sitting position half way between the ceiling and the floor.

The results are better than I expected. The bass is tight without sounding boomy and the room is still lively without sounding bright. I tried extreme toe-in but it caused the bass to sound boomy.
If you have any question please send me a PM. Ron

@paulcreed  In my room, my listening chair is placed against the back wall..with no detriment to the SQ. I have placed absorption panels on the back wall and do have a vault ceiling, which obviously helps. Listening in the near field should allow the speakers to totally disappear in the soundstage, I get tremendous precision of musicians on the stage..and plenty of depth. The hardest part about a small room is the bass response...which will require a lot of trial and error, and in my instance dual small subs. Nonetheless, IME you won’t get very deep bass regardless, although I have managed clean to 35hz.
One other thing you probably will not get is large scale...this seems to be a requirement to large floor standing speakers, which won’t work in these types of small rooms. Precision is the name of the game here, and something I would not want to trade for scale.

It all depends. If its any consolation, I have 2 very different 12X12 rooms set up pretty well these days. One in particular is especially challenging, the other not so much. So yes it can be done. Way more things will work well in a small room compared to a large one. The key to any room offering tight quarters is often that less = more. With that in mind, just try different things and see what works out best.

Whenever quarters are tight and the listening position cannot be far from speakers, I tend to steer away from larger speakers with widely spaced drivers, like many but not all tower designs. Those usually require farther distance to listening position for the drivers to mesh properly.

In my tougher room, my wife’s acoustically challenged sun room with hard tile floor,  lots of windows and cathedral ceiling, I’ve settled currently on a pair of Vanatoo Transparent One Encore speakers (on very short isolating floor stands located near corners and angled up slightly) that work fabulously well in there. They also happen to be the smallest and least expensive speakers I’ve ever tried in there.

My other room is more conventional size and construction (couch near rear wall also) and my main gear is located there. Currently I run a pair of Kef ls50s with a separate powered sub there, but I’ve run many other suitable monitors and floor standers there as well also with very good results over the years.