I've found several instances in which the grant opporunity was listed in the Federal Register, or on the federal agency's website, but it was several days before it appeared on grants.gov. I would hope the lag time will improve in the future, but so far that seems to be the norm.
I have found that if you sign up for the email notifications on grants.gov, that those are received at the same time as they are posted on the site (so you wouldn't have to check daily, just read the daily updates that are sent via email).
