Earlier quoted context omitted.
Was the database designed using transactions to achieve consistency? If so, then you can just instruct Tarsnap to back up the folder containing your database every day, and you're done. If the DB uses transactions for consistency, you can copy it at any time without any problems.
As long as you issue the pg_start_backup/pg_stop_backup pair and keep the WAL logs. If you don't, then you've got a corrupt backup. At least you would catch that problem in your first test restore.
Any database that purports to have consistency must be able to withstand cutting the power to the server at any time. And if it can do that, then it must be true that you can copy the database folder at any time, too, without any special commands. (pg_start_backup is not issued before every power loss, so why would it need to be issued before a copy?)
On the other hand, if postgres doesn't support consistency, then that'd be a major reason not to use it.
EDIT: I'd run the server in a VM and backup VM snapshots. VMware makes this painless (and the snapshotting process is designed to have minimal impact disk I/O performance for precisely the scenario the OP described). VirtualBox probably has something similar. These replies seem crazily overcomplicated in comparison.