Family Security and Small Business Stimulus Act of 2008 - Amends the Internal Revenue Code to: (1) allow a reduced 5% income tax rate on taxable income for low-income taxpayers; (2) allow an advance refund in 2008 for the reduction in the tax rate; and (3) increase to $375,000 between 2008 and 2010 the expensing allowance for small business depreciable assets.