In this 2009 editorial, Bob Barr seems to confirm the notion that Republicans were thinking about a Constitutional amendment when DOMA was passed:
In 1996, as a freshman member of the House of Representatives, I wrote the Defense of Marriage Act, better known by its acronym, DOMA. The law has been a flash-point for those arguing for or against same-sex marriage ever since President Bill Clinton signed it into law. Even President-elect Barack Obama has grappled with its language, meaning and impact.
I can sympathize with the incoming commander-in-chief. And, after long and careful consideration, I have come to agree with him that the law should be repealed.
The left now decries DOMA as a barrier to federal recognition and benefits for married gay couples. At the other end of the political spectrum, DOMA has been lambasted for subverting the political momentum for a U.S. constitutional amendment banning same-sex marriage.
http://articles.philly.com/...
Emphasis mine.
Perhaps in 2009, Republican Bob Barr also mis-remembered what discussions really were surrounding DOMA 23 year prior and any 'political momentum for a U.S. constitutional amendment'. However, taken at face value, Barr's editorial seems to confirm at least the basis of Clinton's claim.
I don't think that, in 2009, Barr wrote this to help Hillary Clinton in 2015.
I think the WaPo Fact Checker needs to do some additional research and perhaps revise their four Pinocchios.