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Obama has already displyed an great capacity to address more than one thing at a time. An investigation would only be distracting to the extent that the media is incapable of that same capacity.
That said, perhaps the most damaging thing that the Obama administration could do is to bleed out parts and pieces of various evidence, as they find them buried in the Bush archives. In the court of public opinion, guilt is often the presumption, and the right would be too busy scrambling to defend than to make trouble.
We are familiar with Republican-style bipartisaship. Now the Republicans need to get a little more familiar with it.