Without having to resort to any browser shenanigans, all Mac users have to do to read any of the New York Times' articles after the 20 articles are consumed is hit the "Reader" button in the location bar. While the New York Times begs you to pay up to read the full story, Apple extracts the text and repaginates it for you in a clean way - the entire article, whether you've paid or not.
The NY Times Warns I'm Almost Out of Articles
What Happens Once You've Read 20 Items
The battle between publishers and news applications has been a push-pull tug of war between innovation and traditional media ownership. One has seen clashes with Flipboard and Pulse as two of the most recent examples, with Pulse even getting sued by the New York Times right after their mobile reader app launched on iPad last year. But technology always seems to win. For every half-baked scheme to force readers to pay for content they expect is free, technology finds a way around it, whether intentional or otherwise.
Clicking "Reader" In Safari Brings Every NY Times Story in Full
Considering Apple's extensive market weight, and Cupertino's highlighting of the New York Times in Steve Jobs keynotes, commercials and other features, I don't see the Times screaming at Jobs to get this particular circumnavigation fixed. It's just another thing it looks like the Times people didn't think about when they tried to force their most loyal (and even occasional) readers like me to pony up.
If you're a Mac user who has switched to Firefox or Chrome, this is one place where Safari has a leg up, so if you hit your limit on the NYT, just open up a second browser.