Currently, Twitter doesn't have a block limit.
Under the current policy, your account won't be suspended if you block 400 spamfollowers in 4 days. The only problem I foresee is if the app implemented by third parties, which you are currently using, does not have robust code to account for a collection much more finite than what was anticipated and returns you with a server error when you request the list of people blocked.
Blocking is not the same as the API limit (180 per hour). The API limit is issue of the number queries to search/tweets per time period, and varies from one application to another. The way it works is that a API limit is proportional to the rate payed to Twitter, which is proportional to the level of usefulness of Twitter integration - a developers' problem, not the least which users need to concern themselves with.