Mitt Romney said "the president cut in half the number of licenses and permits for drilling on federal lands and in federal waters."
According to the Bureau of Land Management, in fiscal year 2011, 2,188 leases were issued for energy development on federal lands. Four years earlier, in fiscal year 2007, 3499 leases were issued. So, not quite a 50% drop, but a drop nonetheless.
However, the biggest drop-off came in fiscal year 2008, to 2,416 leases. The fiscal year for the federal government starts Oct. 1, 2007, so that decline began under the Bush administration. Leases under President Obama took a precipitous drop in 2010, because of the moratorium the administration implemented in the wake of the Gulf of Mexico oil spill, which occurred on federal land and was the worst offshore oil spill in federal history. The number of permits has started climbing since then.
Politifact.com noted the following about drilling on federal lands: "From 2004-08, well into Bush’s tenure, oil production on federal lands and waters fell in four of five years, for a net decrease of 16.8%. From 2009-11, the Obama years, oil production rose two of three years, for a net increase of 10.6%."