My cat just had her first litter...help!

I would call social services immediately. She sounds like an unfit mother. Maybe she has Munchausen syndrome

some mama cats do kill their young. What did the vet say? The only sure way to make sure she doesn't kill them all is to take them away from her and bottle feed them. This involves feeding them every two hours around the clock and is quite an undertaking.

Some cats will kill their young within the first few days if they have been touched or neared by humans, the mum picks up the scent, but obviously you had to near/touch them to get them to the vets! They usually like to go away (cupboard)e.g. somewhere dark and private to have their young (especially first litter) and they should be left until at least the eyes are open or mum will kill them!! Hope this helps but I have been rescueing animals for many years and have experienced this myself.

Cats also kill their babies if they find that they can not keep them. They know when they are physically at their max and if she is unable to feed all, and sees some are starving, nature takes it course.

If she is in too cramped of a place, that might be an issue as well.

Eating the baby, if she is completely reliant on YOU for food could mean she is getting a horrible diet. Give her something organic and not based on corn. Dr Weil has a really good pretty cheap food for cats that has a lot of real animal protein in it. Mom needs iron, blood has iron. She may be eating the dead babies for a source of vitamins.
She may be eating them because that is how they are disposed of too ? Who knows..

Give her better food so she can produce quality milk.
Give her a bigger bed if need be as well

other then that -leave her alone- . Cats survived THOUSANDS of years and MILLIONS of kittens with out us stepping in.
Good luck

Thank you everyone for your ideas and suggestions. Both Momma cat and I appreciate them all