Actually in reading the Attorney General's note that the DOJ will not defend Defense of Marriage - it is really on 1 section they are saying is unconstitutional. They are saying that the Federal Government will NOT defend the proposition that Federal Government defines marriage. It was traditionally left to the states, and goes back to the states now.
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This concerns married pensions, taxes, inheritance etc.
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The Department of Justice said that ONLY this part is unconstitutional and they will not defend it. To be fair, they are turning this back over to the states (which should make all those state right's fans happy). They did NOT say the section that protects each states right to define marriage as unconstitutional. So technically Obama did not say that each state has to recognize each other's marriages (of course this is long established law so it will be struck down in any case). But he is really turning this back over to the states to define.