This is a form of bullying and there's generally three types of responses you can give: walk away, fight back, or simply let it happen.
This basically involves quitting the internship right here and now and accepting whatever grade they give you. It gets you out of having to do that extra work and makes a statement that you won't stand for this kind of extortion but can potentially have a significantly negative effect on your grade, which can have a negative effect on your ability to graduate or find employment afterwards.
This is something that does sometimes happen in the real world too. There comes a time when something is no longer worth the investment and it's time to cut your losses and move on. Companies have terminated contracts with clients and people have quit their jobs over things like this. It's a drastic measure and usually burns bridges so it's not an option to be taken lightly.
I'd only recommend this option if you 100% believe you have a viable means of mitigating the consequences of the worst possible grade the employer can give you. Even then, I'd strongly recommend having a backup plan in case this career path suddenly becomes unavailable to you.
The goal here is to let your manager know that this situation is unacceptable to you. There are a number of different ways you can do this, each with their own pros and cons:
- Standing up to the manager and refusing to do the extra work.
- Going up the chain at your university until you find someone who can step in and help you.
- Re-negotiating the expectations of the project/internship with the manager.
Refusing to do the work
This is essentially taking a hard stance that you won't go beyond what the original agreement was. This position only has strength if there is a written statement of what exactly the work would be, along with evidence that both parties agreed to it. If no such agreement exists, you're pretty much out of luck here. You can still technically refuse to do the work but that would then be flat out insubordination and that'll almost certainly get you fired with a failing grade.
But even with a written agreement, this is still risky. It's very confrontational and quite likely to result in a failing grade just for attempting it. I'd avoid it unless you have some other kind of leverage to ensure you get graded fairly based on the work you did in the scope of your agreement.
Going up the chain at the university
This basically means going above your adviser's head until you find someone who is willing to step in on your behalf and tell your manager this is unacceptable. There is no guarantee that such a person exists, however. There's also a risk that the only person willing to try does not have the authority to actually do anything about it. But if you do find someone sympathetic to your plight, there's a decent chance you can get at least some measure of protection against a bad grade.
Re-negotiating the expectations
IMHO, this is probably your best chance for a win/win outcome. It involves sitting down with the manager and explaining that this new work is essentially impossible to do in the timeline provided with the resources you have available. In a normal working environment, the scope, the timeline and the available resources would all be up for negotiation. In your case, however, it's likely only the scope that can realistically change. Your timeline is essentially fixed by the length of the internship and the resources are also likely fixed, unless they're willing to assign someone to help you. Let them know what you think you can reasonably do in the time allotted and ask if that's acceptable. But be prepared for the answer to be 'no'.
Any reasonable manager is not going to fault you for bringing up these concerns right away. In fact, this is a very desirable trait in an employee because it means you're planning ahead and giving your manager as much opportunity as possible to prevent failure. But that doesn't guarantee that they're going to be able to budge on anything. It's entirely possible that this is work they desperately need done in that time and there isn't anyone else to do it (unlikely, given that it's work assigned to an unpaid intern, but not impossible). And if that's the case, you're probably in a position to ask for some form of compensation for going above and beyond what the original expectations were.
I should note that there is also a decent chance that the manager isn't reasonable and will stick to their guns. It sucks but such people do exist and if that's the case here, this option can backfire horribly. They may or may not fault you for attempting to negotiate. If you feel like they are the type to hold this against you, there's a chance they'll give you the failing grade out of spite. If they're that kind of person, there's not really a winning scenario here for you.
Letting it happen
Basically, just sucking it up and doing the work on the hope that they keep their word and give you a good grade. While this has the highest probability of staying in your manager's good graces, it also sends the message that you will tolerate this kind of bullying and extortion, leaving you open to being subjected to it again.
Sometimes, you do just have to bite the bullet and do something unpleasant to get through a bad situation. Before rolling over, though, I generally like to have reassurance that there is, in fact, an end to the bad situation and that choosing this path will leave me in a position where I have enough control to not have to go through it again. But even if that reassurance isn't available, I might still choose it if I'm convinced none of the other options are viable.
Essentially, my recommendation is to either re-negotiate the expectations if you feel that might work or suck it up and just do the extra work. IMO, the other choices don't have a good enough chance of working out favourably for you to be worth the risk. But regardless of what you choose to do, this is not an acceptable thing for your manager to have done and you shouldn't stay quiet about it. I'd strongly advise waiting until after they give you a grade (and you're certain they can't change it), though. But once you're sure that they no longer have any influence over your grades, I would be telling everyone I know about it. Nothing may come of it but at least the next person to take an internship with them will know what to expect going in.