NEW YORK -- Heather Morgan, an American, and Maria del Mar Verdugo, a citizen of Spain, were close friends for 10 years before they fell in love.

“Always in the beginning, we realized we wanted to be together forever,” said Verdugo.  She and Morgan got married in New York city two years ago with their friends and families in attendance.  “We knew our commitment to each other, but we wanted to make that commitment public, something that even in society’s eyes is a binding commitment to each other,” Morgan said.

They hope to begin a family soon, but Verdugo can’t receive a spousal visa, because she and Morgan are a same-sex couple.  She may remain in the U.S. only as long as her work visa is valid.

“Just beyond the challenges any couple has, we have that complete uncertainty and the idea that at a moment’s notice, Mar could be forced to leave,” Morgan said.

Most Americans married to citizens of other countries have the right to seek legal immigration status for their spouses.  But same-sex couples like Morgan and Verdugo, although they now may legally wed in nine states, have no such right, because of a 1996 federal law - the Defense of Marriage Act (DOMA) - which defines marriage as solely between a man and a woman.

In another part of New York, Venezuelan-born Pablo Garcia and Santiago Ortiz, an American, face the same issue. They have lived together for 21 years and were married in 2011.  Garcia has not been back to Venezuela in that time, even when his father died, for fear of not being readmitted to the U.S.  He doesn’t even like to go out in New York.

“It’s a common expression in Spanish: ‘I’ve been living in the shadows.’  I’m afraid of being deported,” Garcia said.

Thumbing through a huge binder of papers - Garcia’s application for a spousal visa - Ortiz said,  “We applied for his green card, and we got a response saying they weren’t even going to look at the application because we were a same-sex couple.”  He fears he and Garcia could be wrenched apart.

“Right now, his mom’s not feeling well, and we’re very worried about her,” Ortiz said. “And two days ago, his sister called, and said ‘Can he call me, because I want to talk about my mother,’ and going through my head is, ‘Oh my God, is he going to have to leave?  How is he going to come back?’  I don’t know what would happen if he had to leave.”

Both couples are part of a lawsuit seeking equality in immigration rights. They have powerful support on the issue.  President Obama’s immigration reform proposals would grant married same-sex couples an equal right to sponsor a spouse for immigration.  The provision is supported by Congressional Democratic leaders and liberal Latino groups.

Some conservative religious organizations have sharply objected, however, including the U.S. Conference of Catholic Bishops and the National Association of Evangelicals, as part of their opposition to same-sex marriage.  Republican Senator John McCain, a co-sponsor of immigration reform in Congress, has said the issue could doom all immigration reform.

In late March, the Supreme Court will hear arguments in another case challenging the Defense of Marriage Act, which also bars same-sex spouses from receiving Social Security survivors’ benefits and filing joint tax returns, among other rights accorded heterosexual couples.  About 35,000 Americans in same-sex marriages to foreign citizens will be able to seek spousal visas if the Court strikes down DOMA, or if Congress passes President Obama’s immigration reforms.

Morgan and Verdugo said that whatever happens, they will not delay their plans to start their family soon, and they won’t be separated.  Asked how many children they would like, Verdugo said two.  “But we would like to start with one first,” she said, laughing.

Garcia and Ortiz are also hopeful, since a change they never dreamed possible has already taken place.

“It’s the oddest thing in the world, something I never thought could happen,”  Ortiz said of their marriage.  “His mother accepts it, my family knows about it.  When I was growing up, it was a nonexistent idea.  I always saw other people getting married, and that happiness was not available for me.  And then it was.”