Even Republican supporters of immigration reform aren’t inherently opposed to a potential congressional lawsuit against the Obama Administration over the president’s executive action on immigration.

Speaker John Boehner announced Tuesday morning that he was exploring ways to sue the White House on behalf of the House of Representatives over the controversial November executive action, which allowed up to 5 million illegal immigrants to remain in the United States without fear of deportation. While the president’s action was applauded by many Democrats who saw it as a way around congressional gridlock on immigration reform, Republicans have opposed it and accused Obama of exceeding the powers granted to the executive branch in the Constitution.

Freshman Republican Carlos Curbelo of Florida, one of a handful of supporters of comprehensive immigration reform in the Republican caucus, told The Daily Beast that while he would have to see the lawsuit, that “if it’s very specific in seeking to hold the Obama Administration for violating the Constitution, I could support it.” In his opinion, it needed to be “a question of the Constitution not of the policy goals advanced through the actions.” But, while Curbelo noted the lawsuit was not “unimportant, he was more concerned about “an ultimate solution…a series of bills that will address all of our immigration challenges”

GOP immigration reform advocate Mario Diaz-Balart echoed his fellow Floridian. While Diaz-Balart, like Curbelo, said he believes the solution was for the House to pass legislation, he likened the situation to that faced by Congress after former Rep. Bill Jefferson was found with $90,000 in his freezer nearly a decade ago. The House of Representatives at the time reached a bipartisan consensus to sue the government after the Department of Justice searched the corrupt congressman’s office in violation of Article I, Section 6 of the Constitution. As Diaz-Balart pointed out, while everyone found defending the unsavory Jefferson to be politically crazy, it “was an issue of Constitution and law.” He did see a policy crossover between the lawsuit and immigration reform, noting “it’s all interrelated” and “you can’t just remove the issue out of it.” He nevertheless thinks the best way for the House to deal with the matter was by actually passing legislation.

The potential for a lawsuit comes just as the Senate is about to consider an appropriations bill for the Department of Homeland Security, passed by the House, which would defund the Obama Administration’s executive orders on immigration. Every Democrat in the Senate has indicated that he or she would oppose such a bill, which means that barring a compromise, this crucial cabinet department would be shut down at the end of February. A lawsuit might be a compromise to enable House Republicans to fund the DHS while still opposing the president’s actions.

If a lawsuit is filed, it would be the second time that Boehner has taken the White House to court since the midterm election, the first being a November lawsuit over the President’s executive order to delay the employer mandate in Obamacare. That suit has yet to be resolved.