A while after the last census came out, some mainstream university economists recalculated the number of illegal aliens using employment figures...

But Paul Harrington of Northeastern, using his own formula to capture the undercount, thinks the census missed as many as 7 million undocumented immigrants, which he termed a "conservative" figure. By his accounting, illegal immigrants in the United States total 13 million, or 4.6 percent of the population. [Immigrant Tally Doubles In Census By Aaron Zitner ,Los Angeles Times, march 10, 2001 ]

But that was in 2001. Figuring 3 million additional per year (according to Time magazine) we get around 20 million, using advanced calculations involving fingers.