Washington (CNN) One recent summer day, President Donald Trump's lawyer Rudy Giuliani flatly stated that the President would not answer any questions from the special counsel about obstruction of justice in the Russia investigation. Not in writing. Not in an interview. Not at all.

Giuliani could not have been more clear, but there was a problem: other members of Trump's legal team say Giuliani's version of events was wrong.

At the same time, another pair of key attorneys for the President, Jane and Marty Raskin, were busy trying to coordinate calls with a lawyer on special counsel Robert Mueller's team. They continued to negotiate details of that possible deal for the President to answer questions -- including, potentially, about obstruction.

In subsequent interviews, Giuliani went out of his way to clean up his mistake.

It was all just another day in the often seemingly erratic -- and unpredictable -- world of Trump's legal team, which is now into its second set of lead counsels, other new attorneys and nine months of negotiations over the President's testimony.

Despite the sometimes discordant tune from the Trump legal team, the lawyers are close to receiving a round of written questions from Mueller's investigators, according to a source briefed on the talks. The questions and the President's answers would be limited to matters before the 2017 inauguration. The negotiations are continuing on the issue of any potential sit-down interview, which the Trump team still opposes.

And while the negotiations over presidential testimony are moving along, there's a new complication: the possible firing or resignation of Deputy Attorney General Rod Rosenstein, who oversees the Mueller probe. Rosenstein's departure would pave the way for Solicitor General Noel Francisco to take oversight of the Mueller investigation.

Jay Sekulow, one of the president's lawyers, said this week that a Rosenstein departure should trigger a pause in the investigation, including time for the new top Justice official overseeing the investigation to examine possible missteps by the FBI and Justice Department early in the probe. It's likely a new overseer would need time to be read-in to the details of the investigation, but it's not clear what that would mean for Mueller.

Behind-the-scenes lawyers

Giuliani once charged Mueller with trying to "frame" the President in the Russia investigation. Trump himself regularly tweets about witch hunts. Meanwhile, the husband-and-wife Raskins are quietly trying to figure out a way to come to some resolution between Mueller and their client, the President.

Some people close to Trump and lawyers for witnesses question the Trump legal team's strategy, raising concern that it may leave the President exposed to deeper legal troubles at the end of the Mueller investigation. But the Trump legal team is confident about the position they're in and credit that feeling, at least in part, to the legal work of the Raskins, the least publicly visible members of Trump's legal team.

The Raskins, whose small white collar defense firm is highly regarded in South Florida but less known in political circles, are not part of the usual DC suspects called upon to represent and advise presidents. In fact, their hiring in April sent much of the Washington elite googling to figure out just who they were and how they could help Trump.

Multiple sources said that while the President liked the Raskins, the fact that they weren't famous gave him pause. And Trump was bothered by the news reports that he was having a hard time hiring well-known criminal defense attorneys. So the President tapped Giuliani to come on board, not so much for his lawyering -- he has only met with the Mueller team once. Instead his role is more political than legal -- a combination showman, political attack-dog and Trump whisperer.

Behind the scenes, the quiet negotiating sessions have been led by the publicity-averse Raskins, working alongside another one of Trump's personal attorneys, Sekulow, and Emmet Flood, the White House special counsel.

The Mueller team had to adjust to their new legal counterparts -- including Giuliani's public efforts to discredit the special counsel. But the two sides -- the Raskins and the special counsel's team -- have managed to remain focused on the legal issues, with only minimal intrusion from the public attacks by Giuliani and Trump.

According to one source with knowledge, Giuliani's on-air appearances are rarely, if ever discussed. It seems, said the source, that the Raskins are not being held responsible for Giuliani's pronouncements.

The Trump and Mueller teams have met in person at times but much of the back and forth has been through letters arguing each side. As the pace of discussion has picked up in the last few weeks, the Raskins have been talking on the phone with Mueller team members James Quarles and Andrew Goldstein, sources familiar with the matter said.

Jane Raskin and Quarles worked together at the Hale & Dorr law firm in Washington. She also spent time working at the Justice Department, including for a time in Boston where Mueller prosecuted criminal cases. That shared history has fed into the respect the two sides have for each other, according to people familiar with the Raskins' work in the Trump legal team.

The Trump team itself spends more time on the phone than together in person. Giuliani and Sekulow spend more time with the President than the other members of his legal team, according to multiple sources, but all the lawyers have access to their frustrated client when they need it.

A rough start

When the Raskins arrived in Washington last April, they were soon welcomed by leaks of questions the special counsel wanted their client to answer. They set up shop at a local law firm office and tried to get up to speed, only to have the Stormy Daniels case and former Trump lawyer Michael Cohen enter the picture.

It was a rough start, but now the team is in a place not many would have predicted months ago: inching towards a potential deal, in constant negotiations -- which could always collapse -- for the President to answer in writing questions on pre-inauguration collusion between Trump campaign associates and Russia.

Now Trump's lawyers believe they are negotiating from a position of strength. For much of the nine months of talks, the likelihood of Mueller accepting written answers from the President -- akin to a take-home test in college -- seemed distant. Several weeks ago, Mueller seemed to come around to the idea at least in part, but the initial optimism that the sides were close, has now settled into an acceptance the discussions are more plodding.

But there's still a hitch. The deal still in the works would only partially satisfy Mueller's request to interview the President. It leaves unresolved a big question: whether the President answers questions -- written or in a sit-down -- related to matters after the inauguration. It's a matter the Trump legal team still believes is crucial to protect Trump from his own worst instincts as well as the office of the presidency itself.

The Trump legal team maintains the President's inherent powers to hire and fire make those questions off-limits. His attorneys, according to multiple sources with knowledge, believe he should not be asked about his state of mind when making decisions he is inherently allowed to make as the chief executive. Furthermore, they argue, the extensive document production provides answers to anything else Mueller might need. According to a recent book by journalist Bob Woodward, Mueller told Trump's lawyers on at least two occasions at that he needed to question Trump to learn his mindset when he fired FBI Director James Comey, a key element of the inquiry into potential obstruction of justice.

Hug Mueller

When the Raskins entered the picture they were presented with an ongoing "hug Mueller" strategy led by former Trump attorneys John Dowd and Ty Cobb -- a strategy that had been mocked by other attorneys representing other witnesses in the investigation.

The lawyers shared over a million documents and allowed the special counsel team to interview dozens of White House and campaign staff in the outset of Mueller's probe. It avoided the need for Mueller to issue subpoenas, as the lawyers sought to curtail an interview with the President through negotiations.

The additional benefit, the legal team believed, was that the cooperation would build a record that puts the President on a stronger footing in the event of a legal fight with Mueller, should he try to use a subpoena to compel an interview with the President.

"My job was to protect the presidency and guide the presidency through the Mueller process," Cobb said in an interview.

But others have been critical. Trump's current White House counsel, Don McGahn, is known to have questioned cooperating fully and not pushing executive privilege. A lawyer familiar with the strategy said not asserting executive privilege with Mueller's team was "malpractice." The Trump legal team allowed senior White House staff to speak with Mueller's team without limits, including McGahn, who was interviewed for over 30 hours.

But the alternative would have been for the team to challenge Mueller in court and attempt to block or narrow the testimony of staff, a fight Trump's lawyers wanted to hold off on to avoid setting precedent ahead of challenging efforts to talk to the President.

"The benefit to the presidency of proceeding that way was not only to preserve the executive privilege but to ensure the cooperation provided would substantially satisfy the standard set forth in the Espy case in the event there was a subpoena battle for the president. That's exactly where we are now," Cobb said.

That argument, based on a case from the Clinton administration, created a legal test when it comes to a inquiries regarding the President. Trump's team argues that the special counsel must prove it cannot get information from any source other than the President.

The millions of pages of documents, interviews and public records already provided should be enough for special counsel to write a report about the President, who cannot be indicted based on Justice Department guidelines, Trump's legal team argues.

Mueller keeps ticking

"(Trump) is still kicking. So in that respect, it's hard to second guess the strategy," said David Markus, a defense attorney in Florida who knows the Raskins and blogs about the district's white collar issues. "He hasn't been deposed. He hasn't sat down for questions. He hasn't been charged. He is surviving. As a criminal defense lawyer, that's goal number one. I think the lawyers -- not just Marty and Jane -- have been quite successful."

Lilly Ann Sanchez, a Miami-based white collar attorney who knows the Raskins, said they're known for doing work that never makes the headlines. Success for them, means resolving legal problems for a client in a way designed to remain out of the headlines, she said.

"Although Rudy Giuliani has obviously been chosen to be the vocal person for the legal team right now, the intellectual legal work is being done by the excellent lawyers behind Rudy and the President," Sanchez said.

Michael Zeldin, a CNN legal analyst who worked with both Jane Raskin and Mueller at the Justice Department, said the Raskins' style of doing their work quietly and avoiding the media works for them.

"In the end, it is this effort, that will best protect the President's legal interests," said Zeldin.

Sekulow says the Raskins have done a good job implementing a strategy that began before their arrival.

"Their sound judgment and command of the law has been critical in our representation. It is a privilege to work alongside them," Sekulow said.

Giuliani's frequent public comments are sometimes incorrect and require cleanup. But it's had some effect, denting public support for Mueller's investigation. The limitations of that strategy, however, are shown in new polling data. A recent CNN poll shows higher approval ratings for Mueller than for Trump, and 70% of respondents said Trump should provide testimony in the Mueller probe.

But the strategy has also meant containing the President, seething from the investigation he has repeatedly described as illegitimate and meant as a political weapon against him.

At first, the President was appeased by his lawyers who told him in 2017 it would then all be over quickly -- by Thanksgiving, by Christmas, by early in the new year. All of those markers passed by with no finality and the President's anger boiled over in tweets and statements.

Now, again, the timeline is extending. It appears little will be resolved before the midterm election, trying the President's patience and making the election results this November, and the risks of what the Democrats will do if seize control of one or both chambers of Congress, as looming a threat as Mueller himself.