Not in 8 Hours Without Help
3 people * 2 hours of watch each = 6 hours, leaving 2 hours of unprotected sleep. Other answers have given a way to stagger rest to extend the downtime to make it feasible.
Trances Instead of Sleep
If one (or more) of the party is an elf, they only has to trance for 4 hours. So that would mean he could restfully keep watch the other 4, giving 4 + 2 + 2 = 8 hours.
Elf trance does provide some sensory input even while they trance.
It isn't clear if the elf trance is specific trumping the two hour minimum, but it seems Mike Mearls thinks it does: http://www.sageadvice.eu/2016/12/10/what-advantages-does-the-elven-trance-bestow-vs-normal-sleep/
@graysanborn @ChrisPerkinsDnD yes, can also spend long rest awake, on watch #wotcstaff
And so does Crawford, yay it's an official ruling:
A long rest is 8 hours for an elf, but the elf can spend much of it on watch and doing light activity, while others sleep.
After those tweets they released an answer in the Sage Advice Compendium which makes it seem that watching for 4 hours still isn't valid:
Standing watch is even possible during it, but for no more than 2 hours; maintaining heightened vigilance any longer than that isn’t restful. In short, a long rest and sleep aren’t the same thing; you can sleep when you’re not taking a long rest, and you can take a long rest and not sleep.
He does add:
That all said, if you’re the DM and you decide to let Trance shorten an elf’s long rest, you’re not going to break the game.
Animals, Hirelings or NPCs
They could have a ranger's animal companion, or a wizard or warlock's familiar take watch.
Depending on the companion it could sleep while you travel.
With the familiar it isn't clear if the familiar even requires its own rest being a spirit and all -- or if time spent in the pocket dimension counts as rest, etc. etc. But, even it is just another creature to keep watch, you're still better off than having no warning system in place.
You can also expand the party with hirelings, NPCs or the like who could take point/watch a shift.
There are a few spells that would work to help keep watch, for instance:
There are a host of other protection and ward spells, or spells that create safe places to sleep:
- Leomund’s tiny hut
- force cage
- Mordenkainen’s magnificent mansion.
You could always make a house rule that lets the players keep watch 3 hours instead of 2, if they rest 10 hours instead of 8 -- or some such. This wouldn't be RAW, but it also wouldn't be game breaking.
Lastly, I wouldn't hand any of these to the player directly... I would let it be a problem for them to solve and work out. While they do, if they mess up, there is a chance for night encounters with a round of surprise. That would interupt sleep and leave them with two choices:
- Sleep extra in the morning
- Take a level of exhaustion
Each of these could have story implications as well. Maybe they are late to the event they were planing on if they sleep in, and exhaustion can be devastating if they have to perform a lot of skill checks the next day. Used too often, you're a terribly mean DM -- used just right it could be fun.