By Evan Perez, Gloria Borger and Pamela Brown, CNN

(CNN) -- President Donald Trump's lawyers are preparing for a legal showdown with special counsel Robert Mueller, according to sources familiar with their thinking.

Trump's legal team is bracing for the dramatic possibility that Mueller would subpoena the President, setting up a collision that could force a lengthy court fight and test the legal limits of the President's power all the way up to the Supreme Court.

Mueller has raised the possibility of a presidential subpoena in at least one meeting, according to two sources. But some of the President's legal advisers are gambling that Mueller would not go that far. The Washington Post first reported on the subpoena threat.

The already slim chances of Trump sitting for a voluntary interview with Mueller's investigators are growing dimmer, sources close to the President say.

Asked whether the President would ever plead the Fifth Amendment to avoid answering questions, two sources said the legal team believes there are many "constitutional challenges" that would need to be met before that possibility even would be considered.

Trump's lawyers are careful to say that the President hasn't shut the door to a possible agreement for an interview. His new legal team is still assessing that before making a recommendation, sources say.

If Trump refuses to give a voluntary interview, prosecutors could issue a subpoena compelling testimony.

The leaking of a version of Mueller's potential questions for the President, first published by The New York Times, and the President's reaction on Twitter underscore where the issue is moving, sources say.

Trump himself has told reporters he'd speak with the special counsel, and the President's legal team initially claimed that an interview could happen under the right terms.

The President's lawyers said they wanted to finish the interview quickly, claiming it would help end the special counsel's investigation.

But after the April 9 raid of his personal attorney, Michael Cohen, the President's view of sitting down with Mueller had a "seismic shift," according to one source -- from yes toward no.

Many legal observers believe that if Mueller issues a grand jury subpoena for Trump's testimony, the courts will order the President to comply, because the Supreme Court has repeatedly ordered presidents to comply with subpoenas.

During independent counsel Kenneth Starr's investigation of President Bill Clinton related to Monica Lewinsky, prosecutors eventually subpoenaed the president for grand jury testimony. Clinton's lawyers attempted to delay Clinton from speaking to prosecutors for months and told a federal judge they would avoid arguing the issue in court. They ultimately agreed to let Clinton appear before the grand jury without the weight of a subpoena.

In 1974, in United States v. Nixon, the Justices unanimously directed President Richard Nixon to comply with a criminal trial subpoena for the White House tapes. And in 1997, in Clinton v. Jones, the Court directed Clinton to comply with a subpoena for his deposition in Paula Jones' civil sexual harassment lawsuit against him.

Yet if Mueller attempts to force Trump to testify under subpoena -- as many legal analysts suspect could happen -- the sources familiar with the thinking of Trump's legal team say they believe Trump could successfully challenge the subpoena all the way to the Supreme Court.

One of the sources says the legal team views a subpoena for a presidential interview as "precipitating a constitutional crisis."

The Trump team's legal argument, according to multiple sources, is that they believe the special counsel does not have the authority to force a President to appear before a grand jury.

They also believe that Article II of the Constitution, which defines the office of the President, prevents the high court from ordering an investigation into the President's use of his executive powers. In this case, that could include the hiring and firing of persons like former national security adviser Michael Flynn and ex-FBI Director James Comey.

Their political argument also has changed. While the lawyers were originally in a let's-get-this-over-with mode, they now believe that time is on their side -- especially with the 2018 elections looming.

They believe that Trump has done a good job discrediting the investigators and the investigation itself.