According to Felix Salmon, it is not about creating new ideas. Rather, it is about sharing intersting things with your readers, and hoping perhaps that that in turn will be the spark for new ideas.
Firstly, think of it as reading, rather than writing. Lehrer is a wide-ranging polymath: he is sent, and stumbles across, all manner of interesting things every day. Right now, I suspect, he files those things away somewhere and wonders whether one day he might be able to use them for another Big Idea piece. Make the blog the place where you file them away. Those posts can be much shorter than the things Lehrer’s writing right now: basically, just an excited “hey look at this”, with maybe a short description of why it’s interesting. It’s OK if the meat of what you’re blogging is elsewhere, rather than on your own blog. In fact, that’s kind of the whole point.
Secondly, use links as shorthand. Kouwe and Lehrer were both brought down by the fact that they felt the need to re-write what had already been written elsewhere. On the web, you never need to do that. If you or someone else has already written something well, just link to that, rather than feeling the need to repeat it.
Thirdly, use the blog to interact with your peers, rather than just primary sources. There are hundreds of great science and ideas blogs out there already; start reading them, and be generous about linking to them. Your readers will thank you. When you see an article you wish you’d written, link to it and say so. When someone finds a fantastic paper and writes it up in a slightly incomplete way, credit them with the great find, and then fill in the blanks. When two or three people are all talking about the same thing, sum up what the debate is, and explain where you stand.
Fourthly, iterate. Lehrer is a big-name journalist at a major publication: when he writes stuff, people respond, often on their own blogs, and often with very keen intelligence. Link to those people, learn from them, converse with them via the medium of blog, and use that collaboration and conversation to hone and further develop your own ideas. Treat every blog post as the beginning of a process, rather than as the end of one.
There is wisdom there. I find that a good blog post can often fire up the mind, perhaps because the texts are often not long enough to dig deep, yet sufficiently detailed to send you off in some direction or another.