Strengthen the Earned Income Tax Credit Act of 2006 - Amends the Internal Revenue Code to: (1) increase the earned income tax credit phaseout amounts for married taxpayers and make such increases permanent; (2) increase the rate of such credit for families with three or more children; (3) reduce the phaseout of such credit for individuals with no children; (4) make permanent the inclusion of military combat pay in earned income for purposes of computing such credit; and (5) impose an additional income tax on individual taxpayers with adjusted gross incomes over $1 million.