180 miles in a day can be done, as someone already said it's a 300k brevet. For a 300k brevet you'd be allowed 20 hours to complete it, so it would be a very long day.

Whether it can sensibly be done by the group of people you're talking about would depend on their current fitness, experience riding a bike, and willingness to train for it.

The first time I attempted a long ride (150 miles in two days) we covered 83 miles in the first day and by the end of it I wanted to just curl up and die. Those 83 miles took from about 830am until about 8pm, for the second half I had to walk up most of the hills (which did nothing for average speeds), and I honestly didn't think I'd be able to continue. At the time I could cover 30-40 miles in an afternoon and not find it overly arduous but the bigger hills I encountered coupled with doubling my maximum ride length was just too much for me.

A year later I did the same ride and at the end of the first day (about 75 miles, we stopped in a different place) I honestly felt that I could do the same again if I had to. That year we did 150 miles in two days, then had a day off, then 110 miles back (a more direct route) in one day. A few of us did it on mountain bikes.

If your people are reasonably fit and willing to train hard it can be done although I'd say it's not something anyone is going to get through with a "h3ll yeah, I'll give it a go" kind of attitude. Part of the problem is going to be fitness, another part is the sheer amount of time you're spending in the saddle I'm hoping to complete a 300k brevet later this year and thinking in terms of how I'm going to get myself in suitable shape for it. My personal best to date is a 200k.