Let's say you have a project that will involve two web applications (that will share DAL/DAO/BO assemblies and some OSS libraries):
There are two of us with medium estimation capabilities and we won't be able to do it in two days even if we wanted/have to. At least it would be a far off estimate.
Interesting question. I'm afraid the answer is "it really depends!" I know that's not terribly useful (although it IS true) so here are some factors:
1) Quality and completeness of requirements and their specification. This is, to me, most often the project-estimate killer. If you don't have quality requirements, you have no reasonable basis for an estimate. We use a "RUP-lite" style of product development here, so as the engineering manager I won't give anything but the coarsest-grain estimate until we've completed our "elaboration" phase and gotten sign-off from product management that the core 80% of the product features are in fact accurately covered.
2) The scope & nature of the product. Bigger/more expensive/more complicated = substantially longer to estimate. I've spent years working in telco-carrier land delivering solutions which have the normal robust carrier requirements ("5 9's" of uptime required by SLA mean you must really do a good job of solution design and failure recovery!). In that sort of environment with all the moving parts across functional areas of the business, the estimation of work is going to hinge on getting the whole picture...specifically, cross-functional dependencies and external dependencies can be a REAL killer here. That said, I've also built lots of shrink-wrapped and enterprise software, too. In those environments it's much easier as the scope is typically substantially smaller, so thus easier to estimate.
3) How "new" is this project? How "new" is the team to this product or technology set? The newer the product or team, the longer and more buffer you should allocate.
4) How specific do we need to be? If this is a "rough guess" then I'll lean on my engineering leads to provide a conservative estimate, then I'll pad that. If we need a "real" estimate (e.g., one which is used by my boss and which I'll be responsible for hitting), I'd need the input from a number of different managers and team members, who will need time to analyze the requirements and confer amongst themselves.
That can take as little as a couple days, or weeks..it all depends on the size. "Two or three days" is, frankly, not long enough for sizing anything but the most trivial of projects.
The best thing you can do to improve the quality of your estimates to to improve the quality of your requirements, and be ruthless in identifying hidden dependencies.
One final thing: FWIW, I've been doing this since '81 and I regard accurately estimating a project's duration/cost as the single most difficult/fraught with peril part of engineering management.