Told my client last october that I would not be doing a migration.

Two weeks ago they wanted me to do the migration and I told them I will do my best to create estimates but that it was the first time.

Gave them a resonable estimate to migrate the content.

And last meeting they cut the time by 70% to meet the budget.

Fuck the budget, can't pay then you don't get the shiny new toy.

I'm a contractor, not a fucking employee. So all the extra hours are on me.

Going to give them a piece of my mind today.

If I lose this client, i don't give a fuck.

You are right and they fully misunderstood. Don't need to give them a piece of their mind. Just need to point out the stuff in the contract. Either the contract stipulates the work that needs to be done for a fixed rate or the contract stipulates am hourly rate or a combination of both in your favour (minimum amount + overtime with reasonable cap based on unknowns).

In case one you shouldn't even negotiate down. Second model is basically external employment you start doing it if the money drys up you are done no matter the state. In case of both there are some variants and can wiggle a bit where if you are done faster they have some advantage. But they need to understand that they can't get work done for free and that they are happy to do it themselves.