There is a fundamental tension between U.S. 1st Amendment freedoms of speech and press and the 2nd and 14th Amendment right to due process and trial by an impartial jury. In the U.S., the legal profession addresses this through self-regulation; for example, the ABA's model code for judges, rule 2.1, says:
A judge shall not make any public statement that might reasonably be expected to affect the outcome or impair the fairness of a matter pending or impending in any court or make any nonpublic statement that might substantially interfere with a fair trial or hearing.
This sort of obligation is not limited to the judicial branch of government. For example, "any communication by DOJ personnel with a member of the media relating to a pending investigation or case must be approved in advance by the appropriate United States Attorney or Assistant Attorney General."
The guiding principle here is that once someone is formally accused of a crime (and before a verdict is rendered), the government as a whole has a duty to protect the accused right to a trial by an impartial jury. Impartial in this context refers to only deciding a case based on formal evidence presented in the courtroom.
My question is then how congress has acted to regulate its own members in this regard. It was motivated by media reports saying:
House Speaker Nancy Pelosi backed up California Rep. Maxine Waters on Monday, arguing that the Democratic congresswoman “absolutely” did not try to stoke violence by calling on Black Lives Matter protesters to “get more confrontational” if ex-Minnesota police officer Derek Chauvin is acquitted of killing George Floyd.
What mechanisms, if any, exist in congress to sanction members of congress who influence judicial processes through such public statements?