It would create a "Lawful Prospective Immigrant" visa for the 11 million illegal immigrants currently living in the U.S. Those immigrants would have to pass a criminal background check, submit biometric information and pay fees to qualify for the visa.
Republicans and Democrats alike predict that President Barack Obama would fail if he pushed forward with his own effort to overhaul the nation's immigration system and urged lawmakers to hammer out a bipartisan measure.
Mr. Obama's chief of staff Denis McDonough said the White House would only send its plan to Congress if the lawmakers stumble in their efforts and cast its efforts as a backup plan.
"Well, let's make sure that it doesn't have to be proposed," McDonough said of the president's pitch, first reported on USA Today's website late Saturday.
The publication reported that immigrants who served more than a year in prison for a criminal conviction or were convicted of three or more crimes and were sentenced to a total of 90 days in jail would not be eligible. Crimes committed in other countries that would bar immigrants from legally entering the country would also be ineligible.
The proposed plan would also provide for more security funding and require business owners to check the immigration status of new hires.
Those immigrants facing deportation would be eligible to apply for the visa, the newspaper reported. Immigrants would be eligible to apply for a green card within eight years, if they learn English and U.S. history and government, and they would later be eligible to become U.S. citizens.
The draft bill drew immediate criticism from Sen. Marco Rubio, R-Fla. In a statement, Rubio said if proposed, the president's bill would be dead on arrival in Congress.
"It would leave the U.S. with unsecured borders and a broken legal immigration system for years to come," Rubio said.
The senator also said the White House is making a mistake by drafting immigration legislation without seeking input from Republican members of Congress.
The Associated Press contributed to this report.