This is completely wrong. World population is about 7.2 billion people and growth is slowing. The UN projects it will peak at about 9.1 billion in about 2050, then decline slightly. And the US population isn't fast growing, its projected to reach 438 million by 2050. Most of the US growth will be immigration, which is completely under our control.

As for being swamped, lately, in spite of the recent economic downturn, global population growth rates have been lessening by more than demographers expected. All of this can be read with a cursory Google search. My numbers are from the UN, US Census Dept., and Pew Research.