The elephant in the living room is Ted Kennedy’s 1965 Family Reunification Act. legals are abusing this (personal observation), so you know the “new” Americans will do the same.
The Act allows the Newbies to bring over mom and dad and all the other “close relatives”. If they are of retirement age, they immediately go on Social Security. If they are disabled, they immediately go on SSDI. None of them have paid a penny into the system. Next the politicians will say they have to raise SS taxes as the fund is running dry earlier than expected.
You have grasped the essence of why SS is going or is broke. Many people who have never put anything into the the system get to take from those who have ‘contributed’. Politicians haven’t made this an issue and won’t because they know SS is a big scam that has been going on for years. This scam is not just a problem of Mexicans because there are SE immigrants,and European immigrants, and from you call-it immigrants, legal and illegal, milking the free and easy tax money coffers. The politicians blow their political backroom smoke to hide the real source/cause of the a broke SS system.