I'm intrigued by this idea, mainly because I like the idea of a spectrum of success and failure rather than a binary you succeed/you fail, which constantly drives me crazy.
What this makes me think of is a system in which certain tasks have a point value that has to be hit before the effect is complete. For example, a door may have 10 "breakdown points," and succeeding on a Strength check would let you roll your "break stuff" skill die. So we'd replace "Everyone makes a Strength check until someone hits the break DC of the door" with "Everyone who hits a certain DC weakens the door a bit until it breaks." This would let non-specialized characters participate more and could also be a way to differentiate levels of training-- untrained characters get a d4 for effect, trained characters get a +1 to the skill check and a d6 for effect, journeymen get a +2 and a d12 for effect, masters get a +3 and 2d6 (or something like that).
Overall, this would increase swinginess, but maybe that's a good thing as it would remove the entitlement issue of high-mod skill-monkeys walking all over every skill check. It could even replace skill challenges, as many skill checks (Diplomacy, e.g.) would take multiple rolls to earn the points needed to get the job done (the duke has 20 "convincing points" that get worn down as he's turned to your side of the argument). This would eliminate another pet peeve of mine, the super-high Diplomacy/Intimidate check that the players expect will just immediately sway the NPC's mind.
EDIT: In some situations, perhaps you could have a failed skill roll add a (smaller) effect die back to the difficulty of the task. So a failed Diplomacy check would add d4 back to the duke's "convincing points," making the task more difficult to finish out. And perhaps if the duke hit 30 points (having started at 20) he's so peeved that he shuts down negotiations and you've failed the complex skill check. Note that the points added on a failure would always be a smaller die than those removed on a success, to incentivize trying new things and not punish the untrained. Note also this wouldn't apply to everything; failing to break open a door won't really make it harder to break open, it'll just make you look silly in front of your friends.
However, I'm not convinced this implementation would work as intended in all situations-- if a door has 10 hp, why bother rolling a skill check when you could just attack it? But I guess that's always been true about doors.
Oh, and for those to whom this sounds like too much rolling, I hear that, and let us all repeat together as one: IT WOULD BE AN OPTIONAL MODULE!