Is polk Lsi15 too big for my 20x13x8 room?

Your room is not too big for full range speakers played at reasonable levels. That is not to say that it can't potentially be over driven but that applies to most rooms.

I have full range speakers in a similar sized room and have no problem whatsoever not inherrent in the size of the room, which would apply to all speakers (nulls and nodes caused by room dimensions). But, proper set up is critical and your listening distance of 11 feet in that sized room suggests to me that you set up may no be optimum. If you haven't already done so you might greatly improve you sound by doing some research on set up.

Regarding amps and volume to get the music to open up, many dynamic (cone based) speakers sound best at medium to loud volumes. If you like lower volume levels you may want to investigate speakers which present a fuller sounds sound spectrum at lower levels. Remember, everything! has tradeoffs.

Thanks for the input. Can you name some speakers that sound balanced, full at the low level volume? I live in a small town and have no access to anything more than Best Buy and Circuit City.

I can only suggest those things I have listened to at length in my own home - you can check my systems and associated threads for where I've been sonically speaking. So FWIW, I'm presently using Tyler Linbrook Signature 1 full range 1 piece floor standing systems and I'm driving them to my satisfaction with a Primaluna Prologue 3 & 5 (35wt amp). At moderate volume, between 76db and 85 db the sound at the listening position is full, warm, and detailed without being in the least bright or etched. These sound much more full ranged at low volume than any of their predecessors (in my home) with the exception of the Quads, however proper placement, dynamics, and amplification issues keep me from recommending Quads.

The Tylers are capable of playing quite loud and the side benefit with this is, in my system at least, when played loud the highs don't drive you out of the room. I suspect this may have much to do with the tweeter used in this model. There have been a lot of comments on Tylers stuff in this forum and I can hardly recall a negative reaction to them.

For a pair of used Tyler's and if you want to save money a Primaluna Prologue 2 (3800 & 1450 respectively) you can have a great music system that will be hard to beat. And they will sound great in your room which is within 5 inches of the size of mine.

If this is in your budget range, do some more research for confirmation. Tylers can be bought on trial and if you don't like the Primaluna its a dead easy resale item.