Small Business Employee Health Insurance Credit Expansion Act of 2012 - Amends the Internal Revenue Code, with respect to the tax credit for the health insurance expenses of small employers, to: (1) expand the eligibility of such employers for the credit by allowing them to have up to 50 full-time employees (currently, limited to no more than 25 full-time employees); (2) modify the phaseout of such credit based upon increases in the number of eligible employees and the employer's average annual wages as specified in a formula provided by this Act; (3) repeal the requirement that employers make uniform contributions of at least 50% of each employee's premium to qualify for the tax credit; (4) repeal the limitation on such credit based on the average premium in the small group market in the rating area in which an employee enrolls for coverage; and (5) repeal the 2-year limitation on such credit..