Customer X wants the product in 12 weeks or they're going with a competing product. Customer X may be spending 6 or 7 figures with us over the next 5 years in upfront costs and ongoing maintenance and support fees.
You may be saying, "It'll just take 6 months (24 weeks) to re-write this from scratch and do it right" (managers are used to hearing programmers say this sort of thing). For the most part, managers don't care about "doing it right" from a technical perspective, they only care about the bottom line. How is doing it right going to make more money (especially if we loose customer X in the process???)
Also, be careful when making this suggestion. Many programmers who suggest this are simply uncomfortable with other people's code. They can write stuff from scratch themselves, but can't maintain or extend code they've not written (that's always a bad sign). And to make matters worse, they always use the argument "stuff I did not write is horrible".