Asylum (for LGBT and other reasons) is a low-key issue in the press, compared to 1980 when calls went out for private sponsors for Cuban refugees (Dec. 18), especially in southern states. As for policy, it is obviously very sensitive and gets little open discussion.
One "obvious" question could occur in many jurisdictions (including MD, DC and VA, where same-sex marriage is legal (very recently in VA), should someone marry a person from another country so that second person can stay in the country, if the person is otherwise not interested in a romantic relationship? What if the immigrant has children? There seem to be potentially major double-sided moral questions here that have hardly been looked at all in the LGBT community yet.