By Jean-Paul Salamanca (staff@latinospost.com) | First Posted: May 14, 2013 11:26 AM EDT

In an announcement that could signal bad tidings for immigration reform, Sen. Lindsey Graham, R-S.C., stated on Monday that he would pull back from supporting the immigration bill his bipartisan U.S. Senate panel drew up if it includes language supporting same-sex couples.

Via his Twitter account Monday, Graham tweeted the following: "If the Judiciary Committee tries to redefine marriage in the immigration bill they will lose me and many others."

Sen. Graham was referring to the recent push by LGBT groups pressuring legislators to include provisions in the language of the immigration bill that would allow U.S. citizens to petition for green card for their same-sex partners.

Under the Defense of Marriage Act, they cannot do so.

While President Obama has publicly supported same-sex marriage, he has been pressured recently to do more to support provisions supporting LGBT couples in the immigration bill.

However, he has cautioned several times that in this compromise bill from the bipartisan senate panel, not every group would get what they want.

"The bill that they produced is not the bill that I would have written," he said in April. "There are elements that I would change, but I do think that it meets the basic criteria that I laid out from the start ... and I think it's a testament to the senators that were involved. They made some tough choices and made some tough compromises in order to hammer out that bill."

Currently, Sen. Patrick Leahy, D-Vt., proposed several amendments that would allow for same-sex couples to receive the same treatment their heterosexual counterparts do under the bill.

However, that proposal chafes with GOP members who have opposed the inclusions of such amendments. Sen. Graham is not the only one on the immigration reform panel who has expressed reservations about including same-sex provisions in the bill.

As the Huffington Post notes, Sen. Marco Rubio, R-Fla., has also warned that the inclusion of same sex amendments in his legislation would force him to withdraw his support of the bill.

"This immigration bill is difficult enough as it is," Rubio said last month. "If that issue is injected into this bill, this bill will fail. It will not have the support. It will not have my support."

"There's a reason this language wasn't included in the Gang of Eight's bill: It's a deal-breaker for most Republicans," Sen. Jeff Flake told the New York Times recently. "Finding consensus on immigration legislation is tough enough without opening the bill up to social issues."

Still, gay rights groups have continued their push to have language for LGBT couples included in the bill.

"I was troubled to hear hesitation from Senate Democrats," Rachel B. Tiven, executive director of Immigration Equality, a gay rights group, told the Times. "When Democrats are falling over one another to say how they support marriage equality, why are they abandoning gay families when actual legislation is on the table?"