120 degrees F sounds like a dangerous temperature to cook at for so long -- at that temperature you can be incubating some nasty microorganisms -- especially when cooking for a long time. My impression has been that for lengthy cooking 130 F is pretty much the minimum temperature that one can use without the water bath becoming an incubator.
Hopefully Nathan will chime in -- as he seems to have a very good handle on this topic.
So, here is the story.
FDA rules say the lowest you can do to sterilize (i.e. kill pathogens) is 130F, for times given by tables elsewhere in the post (the FDA tables, not my timing tables). But basically 90 minutes at 130F is considered safe by FDA.
FDA says you can be below 130F for no more than 4 hours. So, technically speaking the FDA rules are OK with up to 4 hours at < 130F, but no more.
This is a guideline of course - it is a rule that is sometimes excessive, but sometimes not.
So, if you want to follow the FDA rules, then no more than 4 hours between refrigerator and done if less than 130F. Or, 130F for 90 minutes or MORE.
Does that mean that if you do 122F for 5 hours you will get sick? Probably not, but it is technically outside the rules.
Doing 120F for a really long time could be a problem however