It's OK to ask. You may not get the extension, but given the amount of unannounced lateness teachers often see, asking for an extension in advance with a "how can we work this out" attitude looks like an attempt to be responsible. Contrast with an attitude of starting things the day they're due and then acting surprised when you can't finish a multi-week project in one day.
Perhaps this has more to do with the role college plays in American society. I believe that college has become more of a high school extension than anything, and so maybe it is wrong to blame students who treat it as such. I doubt they would be slacking off in grad school (but I can't be sure!)