In recent years, the Senate has operated under a filibuster rule that 60 votes are needed to end debate and bring an issue to a vote. However, President Trump has encouraged the Senate to "go nuclear" if they cannot get 60 votes in favor of ending debate on his Supreme Court nominee, meaning to change the rules so that a simple majority is sufficient to finish the nomination process.
Tonight on the Senate floor, during a debate on the nomination of Jeff Sessions for Attorney General, Sen. Elizabeth Warren (D-MA) attempted to read a letter from Coretta Scott King that had been persuasive in his previous hearing as part of an unsuccessful nomination to a federal judgeship. However, Mitch McConnell (R-KY) interrupted that reading with an accusation that these words "impugned the motives and conduct" of Sen. Sessions (R-AL), and a party-line vote was held in which Sen. Warren was silenced and prevented from participating in the rest of the debate. A tweet by Sen. Christopher Murphy (D-CT) indicated he might try to continue where Warren left off.
Could the Republicans do exactly the same to Sen. Murphy, and every other Democrat who speaks out, thus effectively bringing an end to debate and preventing a filibuster, with their simple majority?
EDIT: This question is not meant to be specific to one particular confirmation hearing. It is meant to be a broader question about whether or not this particular strategy of silencing the minority is allowed under the Rules of the Senate and applicable laws, as a valid way around a filibuster.