Yes, the idea that Biden is “bringing in” illegal immigrants is indeed a lie, but that is to be expected from the Republicans. They are already here. Ronald Reagan “brought in” three million illegal immigrants by that logic.
About half of these illegal immigrants are originally from Mexico. Most have been here over a decade; many were brought here as children by their parent. Illegal immigration, particularly from Mexico, has declined significantly and in fact the net migration to Mexico has been in the other direction as many Americans have moved to Mexico in the past decade. Mexico is a more hospitable country.