Now that Robert Mueller has turned in the report from his investigation into Russia and the Trump campaign, attention will move from the special counsel to members of Congress. At least five House committees are already investigating the president, his businesses and his associates. Several others are investigating current and former cabinet secretaries and other elements of the Trump administration.

Then, there are criminal investigations being led by federal prosecutors in Manhattan, Brooklyn, Northern Virginia, and Washington, D.C. – plus a state investigation by the New York Attorney General's office.

The world waits to hear the findings of Special Counsel Robert Mueller's investigation into President Trump's connections with Russian intelligence and the Kremlin. CBS News

"We will be seeing a great number of investigations happening at the same time – any one of those is a live torpedo in the water," said Jonathan Turley, a George Washington University Law School professor and CBS News legal analyst.

"So, in many ways the end of the Mueller investigation is just the beginning of even more legal trouble for the President?" asked correspondent Ed O'Keefe.

"Yes. You have to keep in mind, while the Department of Justice policy says you cannot indict a sitting president, it says nothing about holding indictment to proceed after his term of office."

And, Turley said, Congressional investigations will complicate the rest of Mr. Trump's presidency

"Many of these committees were held in abeyance waiting for the completion of the special counsel investigation," he said. "Now that it's done, they have a free field [in which] to operate."

On Saturday House Speaker Nancy Pelosi called on Attorney General William Barr to release the full Mueller report so that committees "can proceed with their independent work, including oversight and legislating to address any issues" raised by the investigation.

Senator Christopher Coons (D-Del.) supports the ongoing Trump investigations, but says when it comes to impeachment, his party needs to be careful.

"Impeachment is a political process that seeks to overturn the results of an election," he said. "There are many other things that, I think, Democrats in the House and the Senate should be focusing on."

For now, Democrats say they will demand Robert Mueller himself testify, which could lead to dramatic hearings just as the 2020 presidential campaign heats up.

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Story produced by Andres Triay.