New IDEA Act or the New Illegal Deduction Elimination Act This bill amends the Internal Revenue Code to deny a tax deduction for wages and benefits paid to or on behalf of an unauthorized alien. The bill also extends to six years the period for assessing and collecting underpayments of tax due to deductions claimed for wages paid to unauthorized aliens. The Social Security Administration (SSA), the Department of Homeland Security (DHS), and the Department of the Treasury must jointly establish a program to share information that may lead to the identification of unauthorized aliens. Treasury must provide information to DHS and the SSA regarding employers who paid nondeductible wages to unauthorized aliens and the aliens to whom such wages were paid. The bill amends the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 to: (1) make permanent the E-Verify Program for verifying the employment eligibility of alien workers, (2) apply such program to current employees in addition to new hires, (3) establish a rebuttable presumption that employers who participate in the E-Verify Program and obtain confirmation of identity and employment eligibility have not violated hiring requirements under such Act, and (4) allow employers participating in the E-Verify Program to make a conditional offer of employment pending final verification of the identity and employment eligibility of the job applicant.