On average about 20% of subscribers are active on a well managed list, so to get 2000 responsive subscribers you need to build a list of 10,000 people.
If you get an opt in of 5 % which is considered as fair (although some squeeze pages with the right traffic can reach 50%+) then you need to drive 200,000 people to your page, so the answer is the length of time it will take you to drive that amount of traffic.
If you track all your traffic sources and continually test and tweak your offer then you should be able to improve on those figures.