Washington (CNN) The Trump administration is facing "limited paths forward" as lawyers explore options for adding a controversial citizenship question to the 2020 census after the Supreme Court ruled against it last week , a source familiar with ongoing discussions told CNN on Thursday.

The options broadly include having President Donald Trump issue an executive order or adding the question as a supplement with the upcoming census, which is already being printed , both the source familiar and a government official said. But the official added that the President issuing an executive order adding the question to the census isn't "realistic" at this point.

"Every single step of the process contemplated by the administration is the stuff of legal fantasy," said Joshua Matz, a lawyer at Kaplan Hecker & Fink, who filed a brief at the Supreme Court supporting the challenge to the citizenship question. "If there is an applicable rule of constitutional law and appellate procedure that this would not violate, it does not occur to me."

Trump tweeted early Thursday that officials were working on the Independence Day holiday to resolve the issue ahead of a Friday court deadline to explain what the government plans to do.

"Department of Commerce and the Department of Justice are working very hard on this, even on the 4th of July!" the President wrote, before departing the White House for his Virginia golf club.

The White House said late Thursday that the President was "looking at every option."

"The Supreme Court ruled that it is legal to have a citizenship question in the census if there's an appropriate explanation -- and it should come as no surprise President Trump is looking at every option within his legal authority to add such a question," White House deputy press secretary Hogan Gidley said in a statement.

The bitterly contested issue got new life Wednesday, when Trump reversed course and publicly said he intended to continue fighting to add a question about citizenship to the decennial population count.

"The News Reports about the Department of Commerce dropping its quest to put the Citizenship Question on the Census is incorrect or, to state it differently, FAKE!" he tweeted. "We are absolutely moving forward, as we must, because of the importance of the answer to this question."

The census is used to set funding for government assistance programs as well as draw electoral maps. Civil rights groups say that asking about citizenship will scare minorities and immigrants, including those legally in the US, away from completing the survey.

Justice Department lawyers responsible for arguing the issue in court were left in the dark Wednesday about Trump's decision to keep fighting, the government official and a source familiar told CNN.

Government officials faced a July 1 deadline to begin printing census forms on the regular schedule, and there was initially consensus among the White House and other top administration officials over the position the Justice Department would take -- that it would go ahead with preparing the census without a line asking "Is this person a citizen of the United States?"

But Trump changed his mind after a hearing Tuesday, according to the source familiar with discussions. Top DOJ officials, including Attorney General Bill Barr, became aware of the pivot before Trump tweeted about it, but lower level attorneys at the Justice Department, including the lawyers who were due in front of a federal judge in Maryland on Wednesday, were not aware of the shift.

"The tweet this morning was the first I had heard of the President's position on this issue, just like the plaintiffs and your honor," Justice Department lawyer Joshua Gardner told Judge George Hazel.

"I do not have a deeper understanding of what that means at this juncture other than what the President has tweeted," Gardner added. "I am doing my absolute best to figure out what is going on."

Civil division assistant attorney general Jody Hunt told Hazel that the Department of Justice had "been instructed to examine whether there is a path forward consistent with the Supreme Court's decision that would allow us to include the citizenship question on the census."

The question has faced multiple challenges. A New York case led to last week's 5-4 Supreme Court ruling blocking the citizenship question from being asked in the upcoming questionnaire. However, the Supreme Court ruling left the door open for the administration to present a new rationale for including it.

The government could file an emergency application to the Supreme Court with an executive order attached, asking the justices to affirm the President's executive authority over the census.

J. Michael Luttig, a former federal judge with ties to the administration, said he believes that the Supreme Court would ultimately find that such an order would be supported by the Constitution.

"Congress has delegated to the President and the commerce secretary the responsibility for taking the census," Luttig said. "Federal courts are required to defer to the commerce secretary's decision to add the citizenship question, unless the reasons he offers in support of that question are unreasonable."

But critics say courts would be unlikely to agree. They contend that while the Census Act vests power in the commerce secretary to administer the census, the president has no constitutional authority to modify it.

"The Constitution grants authority over the census to Congress, rather than the president," said Matz. "The fact that Congress has delegated some role to the Department of Commerce does not mean that the president can independently do anything he wants to the census questionnaire."

Alternatively, lawyers said, the government could take the unusual step of asking the Supreme Court to order the Maryland court to consider the President's executive authority as that challenge makes its way through the system and potentially back to the Supreme Court.

An executive order would likely be challenged in the lower courts and it would be subject to an injunction that would trigger the problems related to timing. And a supplement could complicate the timing for the 2020 census.

Officials are also considering going back to the Supreme Court directly as outlined in court Wednesday, perhaps with some kind of motion to reconsider. That would avoid a lower court injunction, but may not please the Supreme Court.