|The Heroes of the Lance didn't have a 15-minute workday.|
A further complication with this problem is that it means some types of adventures (i.e. journeys) might be played completely differently than short delves or investigations. Part of this, in 3.5 and 4e where map-and-mini combats are the norm, means that DMs are less inclined to have many encounters a day during wilderness treks (or just star-wipe to the dungeon's entrance and skip the journey altogether) because of the set-up involved. But adventures based on longer units of time will have this issue.
I think there are a few ways to alleviate this problem, but not all of them are equally good:
First, encounter-based powers or at-will powers could be made more prevalent. This is clearly a solution tested late in 3.5 (The Binder, skill tricks, all the classes from Book of Nine Swords, etc). It is certainly a viable method. Perhaps a wizard memorizes spells after a short rest, refreshing some all his powers. This is a good solution and quite usable. I like the elegance of the design, but some of it leaves verisimillitude behind.
Second, anti-nova rules could also be in place. Many powers might only work once per opponent or once in an encounter. Martial tricks come time mind here (bluffing and feinting, dirty fighting, dazzling weapon prowess, etc). This is slightly different from encounter powers if there is still a daily limit to them. Alternately, spells might cause fatigue, so that only a few could be used in any given encounter without risking the caster's health. Again, nice, but now we need to be tracking limits as well as number of uses.
Third, daily powers might not all refresh each day. This is crucial for long-term journeys and the like. A distinction could be made between comfortable rests (taken in a sanctuary) versus 'roughing it' where camping might not restore all of your daily resources. This means that a week of rest will leave everyone at full health with a full complement of resources, but one night in the dungeon or restless sleep in a spooky forest might not do it all. I like this idea, but the anthropologist (or Conan) in me knows that 'civilization' is not always better than 'barbarism'. Still, a party is less likely to ask a wizard to prepare and spend all his spells on divinations near the dungeon's entrance and come back to explore it the next day if he won't get all those spells back. And one needn't make a distinction between "primitive" and "civilized" conditions. Ordinary (Camsites and inns) versus luxurious (resting all day in a noble's palace or place of power) migh be reasonable though.
A fourth option, often implemented in older editions of the game, is random encounters and wandering monsters. When you have a chance of being attacked while you rest, choosing your resting sites wisely is quite vital. This option, of course, is easier to implement in systems where the grid and tactical combat can be ignored so you can get through a quick combat in 10 minutes of playtime. I think its also interesting to note that, in earlier editions of the game, this was one of the suggested mechanics in play. It can, of course, be combined with the DM providing strategic places where rest might be easier won though.
The fifth option requires more planning from the DM, and isn't quite a rules option but a story one. This is putting time-limits on your adventures. Waiting a day to rescue the king simply isn't an option, nor is arriving late to the dungeon when rivals might pilfer your booty. This option is great, but much more work on the DM.
Overall, the third option is the one I think I prefer best. Hit points, spell slots, turn undead uses... all of these could refresh at a less than daily rate. The problem is choosing the appropriate rate. Early editions had characters heal 1hp/day, which was far too slow. Fighters would be waiting weeks to be at full health while the mage was healed in half that time. A proportional rate would be ideal, but unless you're dealing with easy bases (halves, thirds, fourths, fifths, tenths) things get a little mathy. Plus, a fixed proportion means every party can rest for a week and surely be at full health, or they can decide they need exactly two days of rest for proper resource management. There's no element of chance.
A dice-based way, then, might be nice if it can be pulled off well. I like the idea of healing based on hit dice, though a rate of one hid die per day of rest still means a fighter with 10 hit dice takes longer to recover than a fighter with one hit die. Rolling all the hit dice ought to result in half, which may be a little high though too. A good system for a spell, perhaps (Cure light wounds cures based on hit dice?) but maybe not daily rests. Wizards might regain a number of spells equal to a die roll (1d6, minimum of your intelligence modifier?), Clerics might regain 1d4 turning attempts, etc. It could get far too mathy, but I bet a system could be devised to keep it to a two-die roll recovery. I mean, there's always the option of rolling percentile dice and consulting a chart, right? Maybe a bit complex, but if you could keep it down to one hit die and one power die... that'd be sweet.
Encounter powers, fatigue from overcasting powerful spells, wandering monsters, and story-limits are also great. I just think that the most effective solution (which also keeps the same sort of resource managment of daily powers) is by not refreshing everything based on the day. And the effort into tracking this itself should be relatively minimal, as the DM could just say that people are fully healed/refreshed after any multi-day rest as needed.