Dan Friedman writes Graham and Schumer initially drafted the framework in 2010 but it failed due to issues regarding feasibility of enforcement.
Schumer said he expects Congress can use the framework as a basis for immigration legislation, which he called a top priority for 2013.
One aspect of the framework would involve creating a path to citizenship for illegal immigrants already in the U.S., he said.
Graham said in the interview the process for becoming a citizen would take up to 10 years.
The framework would also include stiffer punishments for businesses employing illegal workers, issuing tamper-proof Social Security cards and establishing a temporary worker program.