I would say yes. You are treated as a married couple, so if the debt occurred while you were together, you are both equally liable. To the IRS this doesn't mean that you each pay half, it means whoever has the money pays it all. If either is due a refund, they will take it to apply it to the debt.
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Generally, the federal government does not recognize your domestic partnership. If you were legally married to someone of the opposite sex then you might be liable for that person's tax debt.
It will depend on the way the taxes were submitted. If you are not married and didn't file jointly, you don't have any liability.