Would You Take on This Project?

A good (and very large) customer calls you up:

"I've got a really exciting project for you!  This is going to be huge for us and something we will talk up a lot in the media.  The exposure for you guys will be world class! What we need developed is SuperWidgetYYY. I'll explain it in detail to you later but it's really cool, and not that complex.  We haven't got it completely figured out yet but we're mostly there, so we'll be relying on your genius for a little advice in rounding off some areas."

"I have a fixed budget of XXX and I need it completed in the next 5 months because of the strategic and competitive advantage it represents for us.  By the way, if you can't do it, let me know now so I can take it to one of your competitors.  Do you think you can you do it for me?"

After a little more discussion, the basic requirement becomes apparent and it doesn't appear to be that hard.  Yes, there's a lot of work involved and a few unknowns and it will be a bit of a push to get it done on time, but you think that you should be able to deliver successfully if there are no major issues, you can get started right away and assuming that the customer is responsive and available.  You figure you'll probably have to use some of the latest technologies and while budget might be a little tight you think that, yeah, it's do-able.

Now put on your business hat.

Would you take on this project or not?

I'd love to hear some thoughts one way or the other.