That's probably a bit hyperbolic. They've been working on solving this for years, and I had the idea last night when I couldn't sleep. I'm sure it's fraught with problems I haven't considered, but here it goes:
Anyone can use Twitter for free. They will see promoted tweets/trends/accounts, and everything will work just like it does now. Users will also have the option of paying a nominal fee ($5-$10/year) for a premium account. This removes the advertising but also has one more key feature: a premium user can't be mentioned by a free user. Hopefully, this restriction would completely eliminate spam for premium users, which would provide an incentive for free users to pay. There would be some finer implementation details, such as if the premium user follows the free user, or if the premium user mentions the free user first, but that's the gist of it.
This of course hinges on the assumption that a spammer wouldn't pay for the premium account. I can't say for certain that this is the case. I assume they wouldn't link a valid credit card to a spam account, which could be traced to a real person. Even if they did, I doubt it would be worth the money based on the return they get from a single account. Maybe these spam operators also have thousands of stolen credit cards they could use, but for the sake of discussion, I'm going to assume they spam because it's easy and free, and they most likely don't want to be involved in international credit card fraud.
Having users pay for the service is the simplest solution, and it's the whole idea behind other services like App.net. But I don't see them achieving critical mass if every user has to pay, especially not $50/year. To be successful, I think they'll always need free users, and paying should be an option, not a requirement.
Could this work? I haven't thought everything through1, but I think it's possible. As of March, Twitter said they had a 140 million active users. Would 1% of those users pay $10/year for premium features, generating $14 million/year in revenue? I think it seems plausible. I would pay $10/year no question for the current state of things. I would certainly pay even more to have no ads and no spam. I have no clue what Twitter's operating costs are, so it's hard to gauge if that amount would have a meaningful impact. It certainly couldn't hurt, but if it was closer to $25/year and 2-3%, I'd bet you'd be in the ballpark of providing the bulk of their revenue.
1 For one, something doesn't feel quite right to me about separating the "free" users vs the "premium" users, feels a bit elitist.