What kind of major project is this where you're days behind and nobody has noticed or asked about it? That means either there's a lot of trust in you, or it's perhaps not as critical to other people as it seems to you. If it's the latter, you might have a pleasant surprise and find there is more time on the table.
Regardless of all that, the only thing you can do is to be honest and let your boss know what's up.
For future projects, even if you aren't asked for updates I'd still suggest giving them honestly. Even if you're behind - no in fact, especially if you are behind.
Admitting you're behind might feel bad, but it's also sharing responsibility. If your boss knows the project is behind then they also have to help do something about it, be that reprioritising or finding help or extending - and if they can't do that then they're also failing at being a competent boss.