Actually, that’s not entirely true. They approve the absolute number of visas issued, but apparently agencies can then apportion them in different ways using various wiggle room provisions of the law. One of the reasons there are so many illegal Latin Americans is that Obama, shortly after he took office, announced through some agency that all quotas had to be the same so that areas that had produced fewer immigrants, specifically, Muslim countries, could send as many as our neighbors and historic immigrant producers, Latin American countries. Therefore, the legal quota for Latin Americans was restricted.
A country’s immigration law should be based on what is good for that country. We do not need more Muslim immigrants; we barely had any in the past, but already the Saudis are building huge mosques all over the country (including in the city near me, which has very few Muslims) because they know that Obama is going to get them in no matter what. I think many people will be longing for the days when the biggest threat was Mexican day laborers.
A few weeks ago, I actually looked into this with some effort and even as an attorney with considerable experience - but virtually none in this field - I was amazed how complicated the relevant statutes were - probably by design.
There is some flexibility for the administration. I'm not going to deny that. There are some preferences placed on hemispheres, and then some ability to manipulate the country totals inside those hemispheres, and there are "diversity" visas which complicate things. But, these "differences" are measured by the thousand, and not the tens of thousands and by in large, the total number is fixed in stone. Obama - and any president - is surprisingly limited with respect to what visas may be issued for "humanitarian" purposes.