Well, in theory other states would have to recognize the marriages. However, most states of DOMAs. In order for the other states to be obligated to honour these marriages, the DOMAs themselves would need to be challenged and struck down.
Nyet, nyet, to both of you. There is a federal DOMA, been on the books since 1996,
No State, territory, or possession of the United States, or Indian tribe, shall be required to give effect to any public act, record, or judicial proceeding of any other State, territory, possession, or tribe respecting a relationship between persons of the same sex that is treated as a marriage under the laws of such other State, territory, possession, or tribe, or a right or claim arising from such relationship.
There's little reason to challenge the state DOMAs as long as that stands.