The short answer is that it all depends on your yeast strains. Some ale yeasts will go that low; some lager strains like it that high. Personally I am a fan of going to the bottom of the temp range in most (but not all) cases (for example, IMO s-23 is a strain that works better in the temperature range where you have your chamber set right now.)
Now in your specific case, if your ambient temp is 55 then your actual fermentation temp will be higher once things get going. So, you are likely too warm for a lager but you will get beer in the end. IMO you are going to be fine for an ale, again depending on the yeast strain. I did an ESB this weekend with S-04 and my ferm chamber is only a degree or two higher than what you are talking about, and the ale is chugging along like a champ.
I think you will be fine cooling your wort off to around 60 (or however low you can get it), pitch your yeast, put it in your ferm chamber at 55 and let it go. If you are concerned at all, pitch your yeast, wait until you see signs of fermentation, then put it in your ferm chamber and let it go--the actual temp will be considerably higher than your ambient temp. But definitely check the temperature range for your yeast strain before doing this! And if fruitiness is something your after in your ale, cooler fermentation might not be the way to go.