Generally, the Social Security Administration recognizes any marriage that is valid in the state of the SSI benefit recipient's residence. However, the Family Protection Act of 1996 may have changed that general rule in regards to a same-sex marriage that was performed in a state that recognizes it as a valid marriage and the spouses continue to reside in that state. This is a question that may be answered differently in different states or a final "answer" or rule has yet to be adopted or accepted by Social Security.
However, in general, if you are married & receiving SSI benefits, then part of your spouse's income will be "deemed" to you, or determined by SSA to be available to you for your support (used by you to provide yourself with food, clothing and shelter) and your cash benefit will be reduced by that amount. It is also possible that if your spouse has countable (countable by Social Security's rules) resources that you will be over the resource limit and ineligible for SSI benefits even though you continue to be disabled. If you remain disabled to receive SSI cash benefits for 12 months or longer, you will have to reapply for SSI benefits in order to receive them (if you become financially re-eligible) and a new determination of disability must be performed.
"Deeming" rules are fairly complicated.
I strongly advise you to consult an attorney with experience in Social Security disability law in your state of residence and the state in which you were married regarding the issues you've raised.
As you may know, SSI eligibility is based in part upon meeting income and asset limits. If you and your same sex spouse are living in the same household, you may be unable to meet these limits.