Well, there is no hard and fast timing within which you can complete building a CNC router. The answer to this question rather depends upon whether the person attempting to build one is a beginner or has professional experience in making a CNC router or working with it. Other than that, your decision of whether to make a CNC router for DIY purpose, or for potential business purpose determines how much time it might take.
After all, it is worth taking time if your purpose of building the router has a financial cause to it. There could be several other circumstances which might decide the time-frame. However, if you are a tech-savvy individual and have dexterity in CNC router and technology, it won’t take you more than one weekend to get the job done.
If this is your first try towards making a CNC machine, then I would better suggest you to start with something that is easy to build. This way, you will get a fair idea regarding the basics of the CNC router construction. Later, this will help you to build more challenging CNC router models which might take more time (say 5 to 6 weekends) depending upon the project complexity.
If you want to build a DIY CNC router as I mentioned above, then there are numerous short videos available on the internet, which will hardly take you a day to build one, provided that you have all the required parts and accessories for the project.