Healing Requires Healing Surges
As TechImp pointed out in a comment, most healing requires healing surges. Regardless of how great your cleric's healing word might be, it doesn't do anything if the target has no surges.
Surges are only regained when the party takes an extended rest, so the first thing you can do is make extended rests more rare. Throw them into the next encounter, or have things interrupt their extended rest if they don't take the effort to find a safe spot.
Losing a healing surge can be a penalty for all kinds of things, although for story reasons it should generally be something tiring or painful. Some published elements that drain healing surges include monster abilities, diseases, traps, skill challenges, and martial practice component costs. Examples:
Monster
A Bog Hag (Monster Vault) has an aura - Unwholesome Presence - that says "When an enemy within the aura spends a healing surge to regain hit points, that enemy regains only half the normal hit points".
A Black Pudding (Monster Vault) has an attack called Melt. It's effect says "The target takes 2d6 + 14 acid damage and loses a healing surge. It takes 10 extra acid damage if it has no healing surges".
A Rakshasa Archer (Monster Vault) has an attack called "Ghost Arrow". It's effect says "3d10 + 18 necrotic damage, and the target cannot spend healing surges (Save ends)".
Disease
When a player is bitten by a Scurrying Wererat (Monster Vault), they may contract Wererat Filth Fever. The first two stages of this disease each drain a healing surge, and the third stage drains all healing surges.
The disease Blinding Sickness (Dungeon Master Guide) has an initial effect of "The target loses one healing surge that it cannot regain until cured".
Trap
On page 73 of the Dungeon Master's Guide 2 there is a trap (hazard, actually) called Life Eater Haze. It's a gas. Players that start their turn in the gas suffer an attack with this hit effect: "1d10 + 6 poison damage, and ongoing 10 necrotic damage (Save ends). First Failed Saving Throw: The ongoing damage increases to 15 necrotic. Second Failed Saving Throw: The target loses a healing surge."
Skill Challenge
In the Dungeon Master Guide, on page 76 there is an example Endurance check. The penalty for failing the check is losing a healing surge.
Martial Practices
Almost every martial practice in Martial Power 2 requires a healing surge to use it. This isn't something you can do to the players though, they'd have to learn and use the practice themselves. Still, you could always suggest they learn some, not mentioning why...
It's the DM's Job to Balance the Game
If draining healing surges doesn't seem like the right way to go, or if it isn't sufficiently effective, remember that you are the one balancing the game. If they're not hurt enough, have them fight more damaging enemies, or simply more enemies.
A few days ago the party of four 5th level characters in the game I run took out 4000xp worth of enemies in one fight. It took about two hours, they came in waves, and they had some NPC help, but they were clean out of everything but at-will powers by the end of it, and had only healing potions left to heal themselves. They discussed running away more then once, but had nowhere to go and no time to rest. They definitely felt pretty heroic when the pile of nearly 30 werewolf corpses convinced the reinforcements to turn around and run away.
