In late August, Obama administration officials indicated that they view the "family relationships" factor as one that would apply to same-sex couples, meaning that LGBT people could win relief from deportation if they have family ties in the United States. House Democrats welcomed this admission.

"The recognition of LGBT family ties as a positive factor is a critical step forward in identifying key family and community ties to implement common-sense immigration enforcement," the letter said.

The letter makes two suggestions aimed at ensuring this change is implemented. First, it notes that a DHS and Department of Justice working group would be established to review deportation cases and prepare guidance for officials.

But a June memo from Immigration and Customs Enforcement, which is expected to guide field officers, only discusses factors such as family relationship and makes no mention of considering LGBT ties to U.S. citizens.

"We ask that consideration of LGBT family ties be communicated in the guidance being prepared by the new DHS/DOJ working group," the letter said.

Second, the letter asks that the working group include someone "experienced in working with LGBT immigrants and their families to ensure that these factors are recognized and understood."

Republicans have sharply criticized the change in the Obama administration's policy as one that amounts to selective enforcement of U.S. immigration laws.