Microsoft is doing the same what they did with the first Netbooks. Those were also using Linux for cost reasons. Microsoft fought back with cheap Windows XP licenses and they were successful.
Things are a bit different this time, though. There is already a cheap successful Linux based OS available this time - Android. In addition, with Google, Intel isn't fighting against me too Linux distributions but with a company that has a lot of support by hardware producers, which itself helps driver and software integration wise. In addition, Google is about to integrate Android Apps into Chrome OS, which is a very nice add-on for a PC. Once they start to support fully locally installed applications, I think Chrome OS will be much more successful than what Linux was on Netbooks years ago. Especially since Windows 8 is a weak competition compared to Windows XP.
Nevertheless, it all depends on how Google executes. They are doing nice stuff in software, still they are way behind what Apple has achieved. For Microsoft it should be sufficient though ...