Twitter without a short character limit would become something else entirely. "Microblogging" has "micro" in the name for a reason. Without the 140-character limit, it would just become "blogging", and plenty of services exist for that. Microblogging offers an interesting niche, which tends to get used for short messages that often include a URL.

Given that eliminating the limit entirely seems like the wrong answer, I also don't think it makes sense to extend the 140 character limit to something marginally longer; that just seems like pointless churn that would break the expectations of various tools that interact with Twitter and other microblogging services.