The Census Bureau has said that it will "edit" out same-sex marriages from the 2010 Census, purportedly to comply with the Defense of Marriage Act. The Census published a technical note in 2000 explaining why it would count "spouse" responses from same-sex couples as "unmarried partner" responses. At the time, two Census Bureau staffers produced a working paper arguing that "editing" these response in this way was distorting the demographic picture of same-sex couple households.
In 2000, of course, no state legally recognized same-sex marriages (at least not as a general matter, the unusual cases of some transgender people and their spouses notwithstanding), so (as Arthur Leonard notes) the question was merely theoretical (or to look at it in another way, one could assume that same-sex couples saying they were married were not, in fact, legally married). Now, California and Massachusetts do recognized marriage without regard to sex, so adhering to the same policy - even in those two states - means that couples who are in fact legally married in their state of residence will be shown to be "unmarried."
DOMA may or may not require the policy. Arguably, it only prohibits recognition of same-sex marriage for purposes of substantive law, not for the Census. (DOMA's definitional section reads: "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....") Moreover, even if it applied DOMA surely wouldn't bar the Bureau from reclassifying couples as unmarried, but breaking out these couples statistically from other "unmarried" couples, thus largely eliminating the loss of valuable data. If I read the news coverage correctly, the Bureau is in fact keeping track of these couples separately, but not in their published data; in published data, they'll be included with all other "unmarried partners."
Could this policy be challenged in court? Of course, you couldn't just sue for a declaratory judgment on the applicability of DOMA, because the Bureau could have created this policy on its own without DOMA. The Census Clause of the Constitution is really only concerned with counting heads for purposes of apportioning U.S. House sites. Beyond that, Title 13 of the U.S. Code pretty much lets the Census Bureau decide what other information to collect beyond that, so they don't have to ask about marital status at all. Past litigation over the census has centered on undercounting, overcounting, and residence determinations. Unlike those cases, whether couples are counted as married or unmarried doesn't affect the apportionment of House seats, nor is it apparent that it would affect funds provided private or public agencies that are based on population data.
The remaining obvious ground for a challenge is the Equal Protection right of same-sex couples who are legally married in their state of residence. Although the harm to such couples may be purely symbolic, this kind of injury is sufficient for standing if it sufficiently particularized, which it is here. Cf. Heckler v. Matthews, 465 U.S. 728, 737 (1984) (Social Security recipient had standing to challenge gender-based dependency requirement even if it did not affect the amount of his benefits).
The marriage equality movement has generally avoided the federal courts in favor of pursuing protections under state law, for sound strategic reasons. With a federal bench that is more conservative than ever, the chance that marriage litigation would set bad precedent is unacceptable. But might this case be different? The treatment of legally married couples in the Census presents a narrow question that is potentially quite distinct from the federal recognition of marriage for purposes of substantive legal protections and obligations, so that the biases of the judiciary may be less and any negative precedent could be narrowly cabined.
Of course, this was presumably the unsuccessful strategic thinking behind the federal court challenge to Nebraska's broad ban on recognition of same-sex relationships (Citizens for Equal Protection v. Bruning). While the plaintiffs tried to narrowly focus the case on the across-the-board prohibition of any form of relationship recognition, the Eighth Circuit produced a major negative federal precedent on the issue of marriage. One might hope that the Census dispute provides a clearer distinction, but one couldn't guarantee it. So while it seems on the surface that the Census policy could be challenged under the Equal Protection Clause, I'm not sure whether it's wise (from the point of view of same-sex couples) or likely. Which is unfortunate, because in light of the changes in the American legal landscape since 2000 - i.e., that there is now a substantial population of legally married same-sex couples in the United States - the Bureau's policy is almost certainly unconstitutional.