"Amnesty" to me means instant and complete forgiveness. That's not what most people are proposing. Most people, including Bush, wanted some hoops to jump before citizenship.
Definition: Amnesty, from the same Greek root as “amnesia,” forgives past crimes and removes them from the record for future purposes. In the context of immigration, amnesty is commonly defined as granting legal status to a group of individuals unlawfully present in a country. It overlooks the alien’s illegal entry and ongoing illegal presence and creates a new legal status that allows the recipient to live and work in the country.
The Immigration Reform and Control Act of 1986: The textbook example of an amnesty. The 1986 law’s path to citizenship was not automatic. The legislation stipulated several requirements to receive amnesty, including payment of application fees, acquisition of English-language skills, understanding of American civics, a medical exam, and registration for military service. Individuals convicted of a felony or three misdemeanors were ineligible. No one disputes that this act provided amnesty. Supporters said it would be a “one-time” amnesty. It was estimated that one million would apply, but the true number turned out to be 2.7 million.