Please send a few lines from your input file (email@example.com).
What happens when you import the dates to a standard ‘post’ type? Same issue?
For the memory: I think it’s sensible to increase the memory if it’s low. The limit is usually set by your hosting service ( in the php.ini file or elsewhere – you can ask your host). It’s sometimes set very low.
When WordPress runs, it request more memory if the host setting is too low. See the codex entry about WP_MEMORY_LIMIT:
However, WordPress only requests enough memory to run itself. As you add plugins or custom themes, the requested amount may be too small. Imports also consume a small amount for each record imported, which is TurboCSV warns you.