Remember, it's not Trump's office that was raided, it was Michael Cohen's. Although Cohen's name has been linked to the special counsel's investigation - the Washington Post reported in early March that Mueller had "requested documents and interviewed witnesses about incidents involving Michael Cohen" - Monday's raid was the result of information Mueller gave to prosecutors in NY that was not central to that probe.
Moscow has denied USA intelligence agencies' findings that it meddled in the 2016 presidential campaign and sought to tilt the race in Trump's favour.
McConnell also tells reporters he doesn't believe Mueller will be removed.
In addition to facing legal scrutiny for possible bank fraud and campaign finance violations, Cohen is a subject of interest in at least four investigative threads related to Trump, including some within the Russian Federation probe.
The interest in Cohen's communications with Trump suggests that the investigation is delving into the president's actions, legal experts said.
A team at the Department of Justice would need to review any tapes the Federal Bureau of Investigation has seized to determine whether they violate attorney-client privilege and fall within the scope of the search warrants.
Cohen's attorney Stephen Ryan dismissed the raid immediately after it occurred as "completely inappropriate and unnecessary".
The letter demanded they preserve all emails by Cohen that mention Daniels, whose real name is Stephanie Clifford, as well as any emails and text messages related to the alleged relationship.
As the Post noted, when The New York Times reported previous year that Trump had asked Comey for loyalty during a one-on-one dinner and Comey declined, Trump tweeted suggesting that he may have "tapes" of their conversation.
On Monday, FBI agents raided Cohen's NY offices, acting in part on a referral by special counsel Robert Mueller to federal prosecutors in NY. Rosenstein then will determine whether to allow Mueller to proceed or to assign the matter to another USA attorney or another part of the Justice Department. Meanwhile, McDougal received $150,000 from the parent company of The National Enquirer, whose chief executive is a close friend of Trump's.
Records related to Cohen's taxi medallion business were also sought. Critics have said any Trump effort to remove Mueller would amount to interference in the investigation. Mr. Cohen has said he made the payment on his own initiative and used a home-equity line of credit to finance it.
It's not clear what role, if any, Mr. Cohen played regarding the tape, which was made public about a month before the election. On Tuesday morning, Mr. Trump struck back on Twitter: "Attorney-client privilege is dead!" he wrote, "A TOTAL WITCH HUNT!"
The investigation is being run by Robert Khuzami, whose boss, Geoffrey Berman, the interim United States attorney in Manhattan, has recused himself.