In the immediate case, you need to be completely honest with your manager. You need to give a brief rundown of why it can't be done until next week. You need to know what the factors are driving it to be done today. You need to prioritize the work at hand: maybe there's one feature that you could do today that will go a long way with the stakeholders.
But in the long term, this kind of "white flag" scenario isn't sustainable. You need communication with your manager and other stakeholders at every step of the process. You need at least weekly updates to ensure everyone knows where everyone is, what roadblocks there are, and what changes and/or new facts have come up that change scope and schedule.
Now, if this was something that you came in and your manager said "Hachem, we have an urgent fix needed for the Friday night batch job. If we don't, the Acme account won't get processed right and we'll lose their account to our competitor." You really need to find a way to fix that batch job. If you think it will take 40 hours to fix something that's going to run in 12 hours, there's going to be a problem. If it genuinely can't be done, you need to find an alternative plan. Halt this week's process. Remove Acme's accounts from the job. And no amount of pre-communication could have fixed this, at least on your part.
But more commonly, it's more like t Flux Capicator project was a 400-hour work effort. It started in June and finishes today. Your manager says "We've committed to delivering this product today." If you come back and say "It won't be done for another week." it's going to look really bad on your part. As soon as you thought you might not be delivering the product at the time you said you would, you needed to open a communication channel to all stakeholders. If everyone was receiving a weekly status update and a monthly catchup meeting, then you would have spent around an extra 20 hours in meetings and preparing updates, but that's nothing compared to the cost of delaying an application launch.
- right now, find common ground, prioritize the work, make sure you can put other work on the back burner to finish the task as soon as reasonably possible.
- in the future, communicate early and often about the current project status so people are aware of changes to scope and schedule as early as possible.