From their press release reacting to news that candidates Romney, Bachmann and Santorum have all signed NOM's Marriage Pledge:

Log Cabin Republicans strongly oppose the so called ‘marriage pledge’ by the National Organization for Marriage (NOM), which endangers the GOP’s ability to grow and strengthen.

“Republicans got nothing but bad press from the first marriage pledge of the 2012 campaign season, which turned off voters and detracted from our party’s commitment to addressing issues that matter to all Americans. The last thing Republicans need or want is another group pushing the same outdated social agenda under new branding,” said Christian Berle, Log Cabin Republicans Deputy Executive Director.