New IDEA Act or the New Illegal Deduction Elimination Act - Amends the Internal Revenue Code to deny a tax deduction for wages and benefits paid to or on behalf of an unauthorized alien. Extends to six years the period for assessing and collecting underpayments of tax due to deductions claimed for wages paid to unauthorized aliens.

Directs the Commissioner of Social Security and the Secretaries of Homeland Security (DHS) and the Treasury to jointly establish a program to share information that may lead to the identification of unauthorized aliens. Requires the Secretary of the Treasury to provide taxpayer identity information to the Commissioner of Social Security and the DHS Secretary on employers who paid nondeductible wages to unauthorized aliens and on the aliens to whom such wages were paid.

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.