If the conservative justices on the court are honest, then they have to admit that Massachusetts is correct in its claim. DOMA violates the 14th amendment rights of individuals and violates Article Four of the US Constitution. Article Four is the, "full faith and credit," clause of the Constitution which guarantees that the legal proceedings of any state shall be recognized by other states:
Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.
Whereas DOMA states:
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.
Clearly, DOMA excludes one particular type of legal proceeding from being recognized among states which do not want to recognize it-- namely, gay marriage. A strict Constitutionalist (as Alito claims to be) has to realize it's a double standard and that DOMA cannot stand. Even if Massachusetts cannot force gay marriage to be extended in other states, it can force every other state and territory to recognize marriages performed within the state.
Constitution trumps U.S. Code, Mass wins.
What is less clear is if the justices would strike down the entire law or just the particular subsection which deals with states recognizing each other's legal proceedings. If Mass is smart, they'll go after DOMA under the 14th Amendment as well which states in part:
1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
I've discussed why the Fourteenth Amendment and how it has been interpreted by the Supreme Court in various cases is extremely relevant to the gay marriage issue, but suffice to say, the states which bar gay marriage have to prove they have a legitimate, compelling, and unbiased reason for barring gay marriage. They cannot bar it simply because they don't like gay people getting married.
Most difficult is getting the federal government to recognize gay marriage, but if DOMA falls, then the feds may have no choice. This could go either way, but I tend to think the scales tip in the favor of invalidating DOMA.