Yes but the baby can come anytime within a period of about a five weeks and be within the "normal" period. You need an understanding employer to take two weeks holiday "sometime in the next 5 weeks".
It's a very important period where you learn how to take care of the new baby, bond with it, and need to take care of your wife who quite likely is in no condition to do anything other than recover.
(I'm aware that people with very low incomes and no paid holidays at all, may not be able to afford that. But that situation should be illegal in any modern, wealthy country. I guess the answer to the question above may indeed be "yes" in some cases.)
Never being able to take a day off for anything at all is incredibly harmful. People used to fight for these rights. What happened?
Everybody got convinced that a) those rights will be used by those people who obviously don't deserve it and b) those rights will make life harder for them when they become billionaire business owners.
As for what happened, the US isn't highly unionized outside certain regions and trades. Everybody else has next to zero legal protection. White collar workers typically get some leave simply by virtue of having skills that are more in-demand. And the labor movement largely allowed conservative, anti-labor factions to cast them as evil socialists. In the US, "liberal" has long been a bad word.
This is not accurate. If the employer falls under FMLA, then dad gets 12 weeks unpaid leave as just like mom does.
In some states there is paid family leave for both mom and dad. I've used it twice.
Also correct that some states have additional leave requirements. 12 of the 50 have done nothing (only FMLA applies). 14 have lowered the FMLA business size from 50 to something smaller. 7 have adopted more generous maternal leave policies, though most only offer 50% pay over a short period of time.
Only 4 states offer paid paternity leave.
Regardless, the US is the only OECD member that does not require paid maternity leave.