The DMG says six to eight, my experience is closer to 3

The problem is with hit points mostly. A 1st level party member has enough hit points to survive one or two hits from a goblin, but only one Hit Dice. However, the damage is not spread out evenly.

Calculation for 1st level

3 Goblins is a hard encounter on first level for a 4 member party. Depending on intiative they are expected to live three, two and one rounds*, respectively. That means 6 attacks, 2 hits, 11 HP (2x 1d6+2). The Wizard of the party would be unconcious after this, the Ranger not.
Whoever took the damage can spend his only Hit Die after a short rest, but it is gone now. The Cleric could heal him instead, but now a spell slot is spent, so it can not be used in the next fight.

You could send the character without the HD to the back where he is less likely to receive any more damage, but a Paladin is much less effective there. Just like the Sorcere in the front line.

Higher levels

Level 2
A hard encounter is 6 goblins, their expected damage output doubles, but the party HP does not.

Level 6 A two Flameskulls is only a medium encounter, but the Fireballs can take out the party Wizard even if he succeeds on one of the saving throws, and they usually include more than one character. No party can survive 7 more of these enocunters, most could not survive 3.

Level 11 A single Adult Green Dragon is a hard encounter, has a 60-foot cone breath weapon, for 56 damage. Even if the party wins, how many spell slots and hit points would they have left?

All the examples above assume no optional rules, a party with magic items, multiclassing and feats does a bit better.

Conclusion

I have played and DMed in many different groups since 5e came out. My experience is that character deaths usually happen after the third encounter. Hard encounters can't be won without burning up limited resources (HP, HD, spell slots, superiority die, etc) and there are just not enough of them for 6 encounters.

*I am generous here with the PCs, the DMG says a single creature is expected to live 3 rounds on average.

It depends on the types of encounters you plan and what options you leave open. If all of your encounters are combat encounters then the 2 or 3 mentioned in other answers is quite possible. You use up hit points and spells up way quicker during these than during non-combat encounters.

You could pad your combat encounters with near-encounters (party can dodge or hide from the baddies, until at some point they're forced to fight them) that increase tension but won't actually use up too many hit points - unless they fail sneak/hide. Set up scenarios where they can persuade, deceive, or intimidate their way out of situations.

For instance: the party gets spotted just as they manage to lift a grate or door that could be barred. One outcome (perhaps hinted at during description) is that they rush through the opening with the fighters covering ,and then close and bar the door. Some arrows fly through the air, saving throws, but no combat to the death occurs. Narrow escapes can be fun.

Of course later on, you can still run into the bad guys but perhaps at this point they've split up so the really dangerous combat scenario becomes 2 milder ones.

If you allow room for this sort of thing to occur then you can increase the number of tense moments. If the party doesn't go for the non-violent solution or they fail some crucial actions then combat would ensue and they use up a lot more resources.