Why would you need to collect your bags and recheck? Even if this is on separate itineraries, you just give your NH itinerary to UA at LGA/EWR and they'll tag your bags all the way through to SIN. NH departs from T1 at ORD, same as UA.
The only thing you're chancing is weather. Given the last couple of days, I don't know that anything short of staying at ORD for a couple of days would completely ensure you make it. (ie, 3 hours is fine unless the weather gets awful in NY or Chicago)