You finally got something PARTIALLY right.This is what the Appeals Court declared unConstitutional in DOMA and it is the basis of appeal to the High Court:
"In determining the meaning of any Act of Congress, or of any ruling, regulation, or interpretation of the various administrative bureaus and agencies of the United States, the word `marriage' means only a legal union between one man and one woman as husband and wife, and the word `spouse' refers only to a person of the opposite sex who is a husband or a wife.''
SCOTUS could decide the meaning of the word marriage or they could decide to not interfere with Congress by deferring to them for a solution since DOMA was passed by a bi-partisan Congress and was signed by the President.
The SCOTUS could indeed decide the federal govt has the constitutional authority to define marriage for federal benefits. Though it will be interesting to see just WHERE in the text of the constitution those "textualists" like Scalia will find such wording.
But the SCOTUS must ALSO decide whether such a federal definition results in an unconstitutional violation of state's rights and/or equal protection for those couples states decide to marry.
So they could find the Congress has the authority to "define marriage", but that they did so in a manner which violates the constitutional equal protection rights of one class of citizens- i.e. same-sex couples.