In most user cases it shouldn't take longer than 24 hours (much, much less in fact). What type of package are you on and what control panel do they offer you (for example, cPanel)?
If cPanel, you could log into phpMyAdmin and export your database or generate a backup and export the database from that backup. If you don't have cPanel (or phpMyAdmin), you could look for a tool similar enabling you to export databases.
Be sure to check your DB in case it isn't a complete one. In which case contact your host which shouldn't take long at all.