The author of the article mentions "a million different proteins" - The human genome contains about 20,000 genes, each coding for a different protein. Some small fraction of these genes would be involved in cancer, although the exact proportion is an interesting question which we're not entirely sure of. Perhaps with splice variants we're getting into the millions, but obviously you can't consider splice variants to be unique proteins. In any case, the problem is at least 2 orders of magnitude smaller than the author is thinking. Currently, there are 10s of thousands of cancer researchers worldwide, and hundreds of millions of patients, so the studies he talks about are quite feasible.
More troubling is the fact that with the huge amounts of money available, cancer biology attracts a gigantic number of researchers, many of whom are not doing especially great science. There are many, many different pathways in the body that can drive cancer generation, so you can study almost any of them and call yourself a cancer researcher, even though the chances are that most of that work won't lead directly to a cure.
My opinion: cancer is impossible to cure - people will always get cancer. There are deep, fundamental connections between our ability to evolve and adapt to our environment and the inevitability of getting cancer. My opinion on how to beat the disease: genomic profiling of an individual's propensity to develop cancer, early detection, anti-metastasis drugs and improved surgical procedures.
For anyone interested, there is a fantastic review called "The Hallmarks of Cancer", published in Cell that you should check out.