Reagan called it "legalization". The IRCA of 1986 was part of a three prong effort to toughen US border security, punish employers who hired illegals with up to a million fine and to grant a limited number of illegals with citizenship. Reagan's emphasis was on illegal alien employment. Reagan understood, you stop hiring illegals and you stop the vast majority of illegal immigration.
Too bad the Dem's led by Teddy Kennedy had other ideas. Instead of 300K being granted citizenship, 2.7 million were given amnesty.
And it was supposed to be a one-time amnesty.