I agree with the OP and many of the people who've responded that ideally, there would be fast combats and slow combats, with the slow combats generally "boss fights" or otherwise interesting fights (including fights when severely resource depleted) and the fast fights being the unimportant and relatively uninteresting fights (random guards, wandering monsters, etc.) I have found this to be a big problem in a "beer and pretzels" style game that I run--we only get 2-3 combats per session, and that's not enough to get old-style dungeon crawling feel.
I further agree that the solution is to tack on a quick resolution system (perhaps based on skill challenges, perhaps not). The quick resolution system has to meet these requirements to satisfy me:
1. It has to deplete resources in a way comparable to the normal combat system (i.e. in 4E, you have to finish the fight with fewer dailies, less healing surges, etc. than you started with.)
2. It has to have some scalability for opposition difficulty--sometimes you'll be using this for ganking a severely underpowered foe, sometimes for fast forwarding through the tough guards outside the throne room so you can spend your time on the big final battle.
3. It can't be dramatically more swingy than normal combat (halving the hit points and doubling the damage of enemies makes it more likely that a couple of lucky crits will kill a PC outright, which would be frustrating).
4. There should be low to no risk of PC death--I don't want my PCs dying like punks, and in any event it would be frustrating to lose a character in an abstracted simplified way without actually fighting the fight.
"Kill Challenge" sorts of approaches like Flanf's seem promising, but I don't think they quite get the job done. In particular, if you only lose a healing surge on a failure, a medium big fight won't burn off enough PC resources as a kill challenge. A normal fight might cost the party an average of two or three healing surges per PC.
So here's my sketch of a system:
Each PC rolls 4d20. Their rolls plus level are compared to a DC based on the monster's level--something like a target of 10+monster level, with a modifier of, say, +/-3 for every additional monster/additional PC beyond parity. (A party of five 4th level PCs fighting five 4th level monsters would be rolling d20+4 versus a DC of 14; a party of five 4th level PCs versus four 4th level monsters would be rolling d20+4 versus a DC of 11, but if there were six monsters they would be against a DC of 17.) Standard substitutions apply for elites, solos, and minions, and monster levels get averaged out. (Actually, that suggests that it should be calculated off the XP of the fight, which allows a little more granularity. <shrug>)
For each roll, you compare to the DC. If you met the DC, yay! If you missed the DC, you lose a healing surge/quarter of your hit points (your choice which way you take it). If you missed by 5, you lose 2 surges/quarter of your hit points. Each defender can take one healing surge of damage from one other PC. You can spend a daily power to get a bonus of +3 to one roll. (I'm inclined to allow this after the fact, or to do the rolls sequentially? Not sure. You don't want players to have to decide up front before they get either really lucky or terribly unlucky, but speed is essential.) Typically, magic item daily powers, combat appropriate daily utility powers, and level appropriate consumable magic items get you a +2. You can't spend action points, but the fight doesn't count as an encounter for purposes of regaining action points.
The whole thing should take maybe five minutes, start to finish, but still produce something vaguely like the resource burn of hacking your way through the fight.
As should be clear, I haven't playtested this at all. My numbers might be off, maybe even way of. An on-level fight without any daily powers spent should average 3 healing surges per character spent, which seems roughly right--spending a daily power will almost certainly save a healing surge (although that may not be enough of a pay-off for a daily power, but it means that daily powers will mostly get used on screen, which seems right). Also, while some similar system can be used in PF/3.x/other games, you would need to come up with a more nuanced way of handling spell resources (probably something like top level spells are +2, next level spells are +1, etc.--if you only toss magic missiles at a high level combat, you suffer big penalties, thus taking more damage; but the healing economy is very different, too, so...). Ideally we would test the system versus actual combat to try to determine how close it is to accurate, but that would take some work--I might try eventually but I don't have time in the near future.