Not as many people would pay for Twitter as you seem to think.Where are they going to go? Back to email, IRC, or Blogspot? I doubt it. To Twitter's cheaper competitors? How are they going to stay in business?
Rather than just die, Twitter will monetize. Though I doubt that they would monetize by simply charging people to read Tweets. That's much too blunt. There are more subtle methods of throttling the free-account users and thereby encouraging them to pay: limit the outgoing tweet rate, limit the rate of direct messaging, limit the number of followers or followees, lower the number of allowed characters by five for each successive tweet that you write on a given day...
Here's an idea: charge for low latency. If you're on the free plan at Twitter you can make as many tweets as you like and they will be sent to your followers and posted to the public site... eventually. Within, say, 2 hours (or 4 hours, or 8 hours). But if you want instant Tweeting you've got to buy a (fairly cheap) subscription.
Any such change will cause an uproar, so Twitter won't do it unless they have to. But if they have to, I expect they will. They're not just going to fold up and die.