On my touring bike (a New World Tourist, low gear of 20") and my long-distance bike (a Surly LHT with a 13-30 cassette, low gear of 23.5"), I can get down to about 2.5 mph before losing my balance and needing to dismount. On hills where I can't sustain that speed, my usual strategy is to ride, stop a bit, then continue, mostly because it takes more energy to walk and push.

I have been on a couple of hills in Ireland where I could not get started again after I stopped because I threatened to tip over backwards. I walked up those until the grade let up a little bit.