I'm familiar with this problem as it has happened to me a few times. You see, the Internet is a series of tubes. It's not a big truck. Sometimes those tubes get clogged up. Pressure builds, and then a huge burst of data travels down them. Instead of sending a steady rate of 80 or so packets a second, you send no data for a second or two, then something like 160 packets all at once. Try setting your cl_cmdrate to something lower, like 40. It won't make the lag spikes go away, but it should stop you from getting kicked.
This problem is really annoying, but it's not caused by the game. Either your router, cable modem, or ISP is causing the issue. In my case, I switched routers and it didn't fix it, so I might try getting a different cable modem. I have a feeling Crime Warner is to blame here, though, and there might not be anything I can do about it.
