DD was like this. I could NEVER put her down to sleep. I had a lot of 'just leave her to it' comments, particularly from one friend, it then turned out that leaving her daughter to cry consisted of a few pathetic 'uh-uh's then sleep. Her second child was a screamer, I think she understood a bit more where I was coming from.
Anyway - in the baby room (up to 15mo) she would sleep maximum 20 minutes per day. She would sometimes fall asleep on the way home (five minute walk) but sometimes not. She slept pretty well at night which seemed to make up for it.
From 15mo to 2.2years she was in the next room up, where at first she slept quite well (up to an hour a day) but towards the end got way too distracted by the other children and stopped sleeping altogether). She still napped 'at home', for which read 'in the car or buggy'. There was a brief period where I could get her from the car to her cot asleep, but mostly she would wake up soon after stopping moving.
At 2.2 she went up to the next room, which had no scheduled nap, but a quiet time during which many of the children would fall asleep, and they'd be shuffled off to one side to continue snoozing. This suited her so well - she would sleep consistently for 1.5 to 2 hours each day. But not at home - I tried having a quiet time at home and she'd just wander off! Then at about 2.6 she started to play up at bedtime, so we asked them to limit the nap to an hour, and she continued with that until she more or less stopped dropping off during quiet time.
Erm, that was a bit long. But in short - we got by, she wasn't unbearable in the evenings when short of sleep, it didn't seem to adversely affect her nighttime sleep if she didn't nap well, and she DID have periods when she slept better at nursery than at home. AND the nursery didn't expel her (I really worried before she started that they just wouldn't be able to cope with her and I'd have to take her out and give up work). She's been there since 6mo BTW, three consecutive days a week.
Oh, and I found the advantage of a baby/child like that is that, unlike many mums, you don't mourn the passing of the nap, because you never got any free time to yourself anyway.