My Time Machine backups started crawling to an almost halt after updating from Snow Leopard to Mavericks. This took a while to debug and I tried many things, including reformatting my backup drive, rebuilding my Spotlight index, and excluding certain directories from the back up.
In the end what it came down to was a configuration problem in the system that didn’t crop up until the upgrade. The problem was with postgres. It had actually been going on for several years but it didn’t become a noticeable issue until after the Mavericks install.
The final working answer was to open the ‘Console’ app (find it with Spotlight) and look at what was passing through the monitor. A lot of what’s there are debugging system messages that are indecipherable. But watching the console for even a couple of minutes I saw that both my postgres installs were respawning themselves every 10 seconds. This led me to the log file directory for my postgres.
Reading the log file for my postgres I found the same error repeating itself thousands and thousands of times. It pointed me to a misconfiguration in a file, even gave me the line number. I fixed the line, and immediately noticed Time Machine starting to work at a reasonable rate again.
But there was still the second postgres to deal with that was respawning and failing every ten seconds on the console. Since that one was for a postgis project that was long ago completed, I uninstalled it using the postgres uninstaller, called uninstall-postresql. On my system (default install) it was at:
That, of course, knocked it off the console monitor, and now Time Machine is working at normal speed again. So in summary, to get your Time Machine working again, try checking your Console app and use it to trace it back to the problem spot.