Putting Main Street FIRST Act or the Putting Main Street FIRST: Finishing Irresponsible Reckless Speculative Trading Act This bill amends the Internal Revenue Code to impose a .03% excise tax on the purchase of a security if: (1) such purchase occurs on, or is subject to the rules of, a qualified board or exchange located in the United States; or (2) the purchaser or seller is a U.S. person. A "security" includes: (1) any share of stock in a corporation, (2) any partnership or beneficial ownership interest in a partnership or trust; (3) any note, bond, debenture, or other evidence of indebtedness; and (4) derivatives that meet specified criteria. The tax applies to transactions with respect to a derivative if: (1) the derivative is traded on, or is subject to the rules of, a qualified board or exchange located in the United States; or (2) any party with rights under the derivative is a U.S. person. The bill exempts from such tax: (1) initial issues of securities; and (2) any note, bond, debenture, or other evidence of indebtedness which is traded on or is subject to the rules of, a qualified board or exchange located in the United States, and has a fixed maturity of not more than 100 days. The tax applies to transactions by a controlled foreign corporation and must be paid by its U.S. shareholders. The bill allows an offset against such tax for contributions to certain tax-favored savings accounts.