New York Congressman Jerrold Nadler and California Senator Dianne Feinstein have introduced legislation in both the U.S. House and Senate to repeal the so-called "Defense of Marriage Act" (DOMA). The US Congress passed DOMA in 1996. It has two substantive sections: Section two which allows states to not recognize same-sex marriages performed in other states; and section three which prohibits the federal government from recognizing same-sex marriages. The home states of the authors are notable as neither New York or California currently allow same-sex marriages (although New York recognizes marriages performed in other states and California's prohibition against marriage equality has been struck down by the federal courts but is currently being enforced pending appeal).
The Bills (H.R. 1116 and S.598) have been titled "The Respect for Marriage Act" (RFMA). They would strike the original language of DOMA and replace it with a requirement that the federal government recognize marriages that are legal in the State in which the couple resides. RFMA would not require the federal government to recognize a same-sex marriage performed in a state that has marriage equality if the couple resides in a state that does not.
Currently five states allow same-sex marriage: Massachusetts, Connecticut, Iowa, Vermont, and New Hampshire. The District of Columbia and the Coquille Indian Tribe also allow same-sex marriage. RFMA specifically includes the District of Columbia as well as "any other territory or possession of the United States" in it's provisions. The Coquille Tribe is a federally recognized sovereign nation whose lands fall with-in the boundaries of the state of Oregon. Since the Tribe is neither a "territory or possession" of the United States it is unclear if RFMA would require the federal government to recognize same-sex marriages they perform.
The Respect for Marriage Act would effectively codify the February 23rd announcement by the Obama Administration that it would no longer defend challenges to section three of DOMA. Since RFMA would not require states to recognize marriages legally performed in other states it would, in practice, allow section two of DOMA to remain in effect despite removing it from the books; at least for the time being...
Article 4, section 1 of the United States constitution requires states to honor the "public acts, records, and judicial proceedings" of other states, but allows the United States congress to define exactly which acts, records and proceedings are honored. With DOMA congress exercised that power by allowing states to ignore the marriage records of other states. If RFMA passes there will be no federal standard governing whether or not a state must recognize a same-sex marriage legally performed in another state. In the absence of a governing federal law the laws of each state will apply (for instance, both the Texas Constitution and Family Code prohibit the recognition of same-sex marriage so even if RFMA passed Texans in same-sex couples who wished to get married would still be unable to do so). However, under RFMA those state laws will be susceptible to constitutional challenges under article 4, section 1 and the 14th amendments guarantee of "due process under the law" and protections against abridgment of priviledges.
Rep. Nadler filed this legislation last session as well (H.R. 3567). A senate companion was never filed. Last session the bill had 120 co-sponsors including Representatives Sheila Jackson Lee and Eddie Bernice Johnson from Texas. The current version has 108 co-sponsors in the House and 18 co-sponsors in the Senate. Both Jackson Lee and Johnson have signed-on in the House. Neither of the Texas state senators are co-sponsors.