I've been trying to do tummy time regularly with my 2.5 month old son since he was 6 weeks or so. He's never once made any attempt to lift up his head while lying on his tummy - when he was younger, he'd turn it just enough to faceplant and eat his sheets. Now, if he's in his crib, he just lies there and sucks his fist (and starts to cry after a few minutes). If he's on me, he falls asleep.
He is getting better at supporting his own head when he's propped in a sitting position or when he's being carried in the mei tai (which happens most days). I'll keep putting him on his tummy on me to try to prevent him from getting a flat head, but it seems pointless right now to continue with the tummy time in the crib / on the floor.