As the immigration overhaul process accelerates in Congress, expect specific constituencies with a stake in the outcome to begin signaling their demands for support — as well as grounds for joining the opposition.

The latest to speak out was a collection of leading advocacy organizations for individuals who identify as gay, lesbian, transgender or bisexual. In a joint statement released Wednesday afternoon, these groups reiterated support for comprehensive changes to federal immigration law, but they made clear they could oppose legislation that they feel discriminates on the basis of sexual orientation. The following was issued by the National Center for Lesbian Rights, GLAAD, National Gay and Lesbian Task Force, United We Dream and Queer Undocumented Immigrant Project:

“Our primary goal is to pass a commonsense, compassionate immigration reform bill that puts our nation’s undocumented men, women and children on a pathway to citizenship. That pathway would provide at least 267,000 LGBT undocumented people the opportunity to become full participants in our economy and our democracy. We do not believe that our friends in the evangelical faith community or conservative Republicans would allow the entire immigration reform bill to fail simply because it affords 28,500 same-sex couples equal immigration rights. This take-it-or-leave-it stance with regard to same-sex binational couples is not helpful when we all share the same goal of passing comprehensive immigration reform that provides a path to citizenship.”

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Tuesday radio interview

“This immigration bill is difficult enough as it is. There are already enough questions being asked, questions that need to be answered, legitimate points that are being raised. If you inject something like this in the bill, it will die,” said the Florida Republican, a tea party stalwart who is considered the linchpin to the deal.

Currently, there is scant evidence that this issue will rise to the level of threatening the prospects for an overhaul this year. For Republicans in particular, accepting a bill that grants illegal immigrants with a pathway to citizenship remains the most politically sensitive issue to deal with. But as more and more Democrats have publicly announced their support for same-sex marriage, the possibility of this issue rising to the fore can’t be dismissed out of hand.

Here’s what else the coalition of LGBT groups had to say Wednesday afternoon:

“We all deserve a chance to live with dignity, to pursue our dreams, and to work for a better future and better quality of life.

Our current immigration system is broken. It dehumanizes, scapegoats and vilifies all immigrants, including LGBT immigrants, and their friends and families. Comprehensive, compassionate immigration reform is an urgent priority for our nation and the LGBT community.

We stand firmly that the following principles must be included if we are to truly have comprehensive immigration reform legislation:

• Provide a pathway to citizenship.
  

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  Ensure that family unity remains at the heart of immigration law and policy.
  
  

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  End unjust detentions and deportations.
  
  
  

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  Uphold labor and employment standards and ensure that the enforcement of immigration law does not undermine labor and employment rights.
  
  
  
  

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  Promote a dignified quality of life for border communities by establishing oversight mechanisms to ensure border agencies uphold basic civil and human rights protections.
  
  
  
  

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  Ensure immigrant members of our community are not relegated to permanent second-class status.”