Testing more with level 6 characters, it seems like Moderate (level + 1) encounters are more or less the optimum level. Each seems to drain about 1/6 of the party's resources. Since resources are drained unevenly, the party probably wouldn't be happy with 6 encounters, but should be able to handle 5 in a day. Given normal player caution and the desire to be able to handle "wandering monsters" while sleeping, 4 encounters per day would be normal.
The proper mixture for throwing in harder encounters is a bit trickier. It is easy to make the big fights too easy or too hard. I'm still trying to figure this out. I think that when players are throwing around huge daily powers, a little bit of luck or toughness on the monsters' part can make a big difference in whether they survive the initial onslaught. The players can suffer a lot of damage if the fight drags on for a long time after they have run out of powers.