You might have already started on this, and if you have then what advice I'm about to give now is going to be too late, but maybe I can offer some help in solving problems.
The main problem of running something like this based on a film is that you might be very inclined to lead your players around by the nose, and even fudge die rolls so that they don't get too badly hurt during the adventure. Try not to do this if at all possible.
Secondly, The Big Lebowski is a reiteration of The Big Sleep, in which the detective goes around looking for the wayward daughter, or in this case wife, of a wealthy man in a wheelchair, and find the people who are behind it. The Coen Brothers did a fine job, even if, in the end, nothing really happens. The nihilists and the Big Lebowski both tried the play each other for fools, and neither of them achieved what they were after. And the Dude got his car destroyed, one of his friends dies, and he's basically back where he started, except that he's got a child on the way that he'll probably never see. The point here is that a session where nothing, in the end, happens, even if the PCs get experience for it, might rub them the wrong way.
The best thing to do is to change up The Big Sleep scenario a bit. You can have a kidnapping that involves something lewd, a wealthy but crippled patron, and lots of intrigue from various angles, leading up to a showdown in the end. You should watch The Big Sleep (with Humphrey Bogart) and Harper (with Paul Newman) for more information. Harper is The Big Sleep, with some variation.