Kentucky Gov. Steve Beshear and Attorney General Jack Conway are asking a federal judge to deny summary judgment—and an immediate injunction—in a lawsuit challenging the state’s same-sex marriage ban.

In December, Louisville residents Greg Bourke and Michael De Leon asked a federal judge to issue a ruling and implement an injunction against the state’s ban on same-sex marriage. On Monday, Beshear and Conway asked the judge to deny Bourke and De Leon’s request.

But an attorney representing Bourke and De Leon said he believes Beshear and Conway are secret supporters of their cause.

“It’s the plaintiffs’ position in this case, and it has been all along, that Kentucky’s laws prohibiting same-sex marriage are unjust and unconstitutional,” Canon told WFPL. “I think that the Beshear administration knows that, and the response that they filed yesterday tacitly acknowledges that.”

Conway’s spokeswoman said it’d be inappropriate for the attorney general to express personal views on a matter pending in court. In 2010, then-Senate candidate Conway opposed same-sex marriage.

In a statement, Beshear deferred to the 2004 referendum approving the state’s same-sex marriage ban, saying voters “have made the decision for the commonwealth.”

Beshear and Conway declined to address this week’s filing because it’s pending litigation.

Canon said he’s not sure when the U.S. District Judge John Heyburn will make a decision on whether to issue a summary judgment or decide on an immediate injunction. He noted that judges have cleared the path for same-sex marriage in other states. (Here’s a state-by-state map from same-sex marriage supporter Human Rights Campaign.)

Bourke and De Leon met at the University of Kentucky and were married in 2004 in Canada. They have two children. Bourke is also running for a Louisville Metro Council seat.

In the lawsuit filed in July, they argue that Kentucky’s same-sex marriage ban violates several provisions of the U.S. Constitution, including (but not limited to) the Equal Protection Clause. In their filing Monday, Beshear and Conway dispute that the state’s same-sex marriage ban is unconstitutional.

(Both filings are at the bottom of this post.)

“Slowly, piece by piece, the entire country regardless of how traditionally conservative they may be thought of as being, the whole country is moving in the direction of marriage equality,” Canon says.