Oftentimes, directors and actors are not as aware of this as you'd think. The producers should be more active in preventing this sort of situation (but it is a tough balance between that and keeping your stars happy and allow your director the artistic space).
Actors and directors focus more on their work than on the budget or time, but I'd like to believe that they'd be reasonable enough if you gently reminded them that the budget and time limits do exist, as well as early press (but this sounds more like an information leak that no one intended).
But you know, there's the general debate on, if a director has a specific vision, should he not comprimise? My personal stance is that any art, especially filmmaking, should be about what you're able to do creatively given certain limitations. I think it's dangerous when a director is allowed to go wild and do everything he wants exactly how he wants it. Does it produce a better film? I don't think it does. SOME filmmakers, like Kubrick, do seem to demand this. Kubrick knew that time was his most valuable asset, though, and as I understand it, pretty much had a deal with Warner Bros that said he could take... quite a while to make Eyes Wide Shut. That's an example of a film that couldn't really be made any other way, but BUSINESS-WISE, it didn't make much sense. Eyes Wide Shut didn't make much of a profit for Warner Bros, although I don't think it lost any money, either.
Of course, this is just one publication, with one source who seems to get an unhappy vibe from the set. Maybe it's not as bad as it sounds. I hope the movie turns out well.