Former senior special agent of the INS Michael Cutler testified before Congress recently regarding the titular question:

...If, for argument sake, we figure on a number of 15 million illegal aliens, or ten times the number that had been estimated prior to the amnesty of 1986, and if the same sort of under counting occurs and if a comparable percentage of aliens succeed in racing into the United States and making a false claims that they had been here for the necessary period of time to be eligible to participate in the amnesty program that the Reid-Kennedy provisions would reward illegal aliens with, then we might expect some 35 million illegal aliens will ultimately participate in this insane program. Once they become citizens they would then be eligible to file applications to bring their family members to the United States, flooding our nation with tens of millions of additional new lawful immigrations while our nation’s porous borders, visa waiver program and extreme lack of resources to enforce the immigration laws from within the interior of the United States would allow many millions of illegal aliens to continue to enter the United States in violation of law...

Previous testimony from him was featured in The Senate amnesty: an "Administrative and National Security Nightmare"