States could take the tax credit approach a step further by making them fully refundable so that low income families whose tax liability is less than the credit would receive the remainder as a tax refund.
If you filed your 2011, 2012, and 2013 IRS taxes late around March 2015 and had a refund due for 2011 and 2012 that you filed as applied to the next year's taxes, rolling it forward each year until 2013 with remainder for 2014, is this allowed?