My party has played from levels 1 to 7 from all custom material. So far I find a party member drops below zero on average once per two sessions. Given the 3 strikes till death rules though I've never seen a character die. They pretty much have an average of 6 rounds to live, which is plenty of time to get them back to life. I'd say that 4E gives the threat of death to players, but not the reality of it.
Don't get me wrong though 3E is no different if you take out save or die. In my history of 3.X, I've never seen any character in any campaign die from non-save or die/save or kill yourself effect. It always ends up with the same old unconscious, have about 3-5 rounds to live, and the cleric heals you up to full health in 2-3 rounds if not only just 1. I'd say healing in 4E is even less forgiving than it ever was in 3E assuming you had a cleric in the party.
To fix the issue in 4E though...
Within the rules you can have the mosters attack (but not coup de gras) downed characters until they are either saved or die from exceptional damage. This would effectively speed up the clock from the death saves.
I would NOT lower the heal surge values since that probably promotes resting which grants more use of daily's and actually powers up the party more.
With game rule modifications you can do a lot. You can do something simple like change the 3 death saves rule to just 2. You could remove the death saves rule and replace it with something like, "Roll a d20, a natural 5 or lower means you die, 6-19 means no change, 20 means you stabalize".
One idea I like (but don't personally impose) is you could use negative hitpoints as a form of long term damage and heal it as you would ability score damage in 3.X.
For example, I have a character with 50 Max HP and he is knocked down to -10. His max HP available is now 40HP. The next day, his max HP becomes 41HP...and every day after it will increase by one to reflect the long term wounds. This could prove harsh because in 3E even ability damage could be healed either right away or after one night. But I think this has the most style and would provide the most 'fear' in the PC possibly causing them to alter strategies in combat to stay safe.