By Kristina Sgueglia, CNN

New York (CNN) - A New York woman releases a deep sigh of relief as she reflects on a court ruling that her spouse will not be torn from her by the looming threat of deportation.

"Now we can make plans, and we have all the time in the world," Cristina Ojeda, 26, tells CNN.

Monday, she received a letter confirming the ruling by Immigration Judge Terry Bain that will allow her wife, Argentina-born Monica Alcota, 36, to stay in the United States, according to the couple's attorney, Lavi Soloway.

Soloway said this is the first time the government had asked an immigration court to close removal proceedings against a spouse in a same-sex couple since the Department of Homeland Security announced November 17 that a "working group" would be reviewing all pending immigration cases.

The group began the process of identifying and closing "low priority" deportation cases three days after Soloway submitted the request to close Alcota's immigration case, the attorney said.

"We're really gratified because we feel that government moved in the right direction in the time we needed," Soloway told CNN.

He made the request to halt deportation based on Alcota's marriage to Ojeda, who is a U.S. citizen, and on Alcota's "strong moral character, family presence, and deep ties to members of the community." Alcota lives with Ojeda in Queens, where she restores antiques.

Until Monday, life for Alcota and Ojeda had been put on hold for two years.

Alcota had been living in the United States for more than 10 years since overstaying her tourist visa, when she was pulled off a Greyhound bus in July of 2009 and taken into a detention center in Elizabeth, New Jersey, Ojeda explained.

Ojeda, a social worker in Queens, traveled two expensive hours by subway, bus, train, and sometimes cab - there and back every day for three months - to see Alcota.

"Looking back on those days, we have come so far, we have accomplished something really big," Ojeda said.

The couple was married in Connecticut in 2010, before New York law allowed same-sex marriages.

"We have gone through a really rough road these past two years. The burden was horrible. We never knew what was going to happen," Ojeda said.

"We lived in fear we were going to be torn apart," she told CNN.

While celebrating their success, Ojeda said "the battle is not over."

She told CNN that Alcota's effort to be granted a green card, which was originally denied, now has been submitted for appeal.

"Of course, we will not have full equality until DOMA is gone," the couple said in written statement.

The Defense of Marriage Act bans federal recognition of same-sex marriages. The act also says that states cannot be forced to recognize such marriages performed in other states.

Despite the battle ahead, the happily wed lesbian couple is excited to have their life back.

"At least we have this. We know she is not going to be taken away, we can live our lives a little better, we can do things we haven't been able to do," an emotional Ojeda told CNN between joyous gasps.

The couple is even turning over the idea of renting a new apartment and perhaps getting a new car.

CNN's Kristen Hamill contributed to this report.