To be sure, should the Republicans lose control of either chamber of Congress in November, it's possible that the president's fortunes could shift. The president's public relations strategy "only works well when we have a majority in both houses, and a Democratic House could make his life miserable," said Ryan Williams, a Republican political strategist and former spokesman for Mitt Romney.
If Mueller does uncover any damaging information about the president, it is likely that any ramifications would play out in the political realm, where voters and Congress will decide on the president's fate.
Robert Ray, who succeeded Kenneth Starr as the independent counsel investigating former President Bill Clinton during the Whitewater scandal, said the clock is ticking for Mueller to end his investigation.
"I do not think that the president's strategy is that much different than what you saw during the Clinton era, and it's understandable," he said.
The investigation into Clinton was widely seen as a boon to the president's support among voters, as Americans responded negatively to the perceived partisanship of the Republican Party. When the House of Representatives drew up articles of impeachment against Clinton in 1998, his approval rating hit an all-time high.
"When you reach the point of 18 to 24 months, that's about how long you have," Ray said. "Is public sentiment here a factor in the course of an investigation involving the president of the United States? Absolutely."
It's a tricky line to walk for Mueller, Ray said, because typical white-collar investigations can last far longer than two years. The political time constraint can be a severe limitation.
Giuliani has called on Mueller to wrap up his inquiry into whether the president has obstructed justice by September, in advance of the contentious November midterms. Mueller was appointed to oversee the investigation into Trump and his associates' alleged links to Russia in May 2017.
So far the special counsel has secured five guilty pleas, including from the president's former national security advisor Michael Flynn and the deputy chairman of his inaugural committee, Rick Gates. Trump's former campaign chairman Paul Manafort is currently facing trial in federal court in Virginia on charges brought by the special counsel.