"The big companies paying the extra tax will increase prices, because that is how real life works"

You're so conservative it blinds you. 

Corporations might raise prices.  They might not.  If they got a tax cut they would keep prices the same and take more profit.  If they get a tax raise, it's equally possible they will keep prices the same and take less profit.  After all, every company theoretically sets the maximum price it thinks it can get on the free market to maximize its revenue (why leave money on the table indeed), and if competition prevents them from raising prices past a certain amount before customers go elsewhere, that will be the price cap, regardless of taxes.

But please, tell me more about the "real world."  How many times did we hear prices would skyrocket thanks to an increased minimum wage? Studies in Seattle have concluded that predicted effect (a long time conservative canard) was minimal to nonexistent.