A. geek estimate "couple of days" -> two weeks
B. geek estimate "couple of weeks" -> two months
C. geek estimate "couple of moths" -> six months
I don't mean that in a nasty way. The "geek" or technical estimate does indeed take that time - for example the core technical work in the first example does get done in a couple of days in the zone. But there are complications, there's polishing off, there's testing/scaling/deployment/troubleshooting and, unless you are very very lucky, there are other things to do.
Of course there is a significant error in such rough binning, but it comes out in the wash over the life of a project.
Anyway I would say your example is a type B if you are starting from scratch and lack the necessary know how, or type A if this is something you have done before.