That is certainly part of it. You also have to add the cost of the lobbiest the shipyard hires to get the money and the board seats and executive positions it has to give to retired admirals and politicians.
Another big factor is delay. A ship of this size takes up valuable realestate during the build process, teams of men and equipment waiting for other parts to be completed. Parts taking up room in warehouses. American shipyards do not have the fluidity of overseas yards, no do they have same levels of productivety. When a project pauses many of the components grind to a halt but still need to be paid for.
The cost of steel may not be a problem but the finace charges and interest payments and storage cost of that steel when a delay happens can be huge.
Capital cost is another factor. Finance types like to minimize risk and, because of the sheer number of workers and material, shipyards have large financial needs. They have to borrow money often and the bankers charge higher rates for money based on risk. Will congress cancel the project half way through? Will congress open an investigation on delays and charges? Will budget sequestration grind everything to a halt? Will the governmwnt pay for the delays caused by congress? Will the uscg change design plans part way through based on new threats or a new mission set out by the next commandant? Will third parties sue or charge the shipyards overages based on government delays? Will an USCG Admiral or Class executive or senator put up road blocks because the third party company he has an i terest in was not selected?
Many shipyards overseas (And one US company: edison chouest) do everything from drawing up the design to fabricating equipment, in house so they are not reliant of thrid parties who can threaten delay or overage charges in return for favorable concessions.
The unknowns in these questions increase the level of risk and bankers always charge more for money lent against higher levels of risk.
Another cost are government subsidies. I can’t go fully into this factor here but modern economists agree that even the best subsidies end up costing the company that gets them more than they recieve.